principal . When amount of money deposited or borrowed is W the HY? Ininterest the isReal earnedWorld or paid only on the principal, it is simple interest . The u calculated discounts, You’ll calculate simple of the principal So you canearned find the amount of per a annual interest rate is the percent or paid arkups, sales tax, and tips. interest. security deposit, as in Ex. 19. year. The sum of the interest and thelend principal is called the balance . Family Loan Tim’s parents Tim
Now
EFORE
nts
$100 so he can buy a radio-controlled In airplane. the Real They Worldcharge Tim 5% simple annual interest. Whatlend will be the total Simple Interest Family Loan Tim’s parents Tim $100 so he can a radio-controlled amount thatbuy Tim will owe his parents Words Simple interest I is the product of the principal P, the airplane. They charge Tim 5% simple in 1annual year? interest rate r written as a decimal, and the time t in
annual interest. What will be the total years. amount that Tim will owe his parents The amount earned or paid for the use of money is called in in 1 year? Algebra I ! Prt amount of money deposited or borrowed is the principal . W The amount earned or paid for the use of money is called interest . The interest earned or paid only theprincipal principal, it for is simple i Numbers A $500 deposit 6%on simple annual interest amount of is money deposited or earns borrowed is the . When 4 years. I ! ($500)(0.06)(4) !the $120 annual rateonlyison the percent principal o simple interest earned interest is interest earned or paid principal,of it isthe . The annual interest rate the interest percent of and the principal earned or is paid per the b year. The sum ofisthe the principal called year. The sum of the interest and the principal is called the balance .
EXAMPLE
1
Finding a Balance
Simple Interest Simple Interest
To find the total amount that Tim will owe, as described above, first find the interest theinterest simple Iinterest formula. Wordsusing Simple is the product of the principal P, the Words Simple is theformula. product of tthe annual interest rateWrite r interest written as aIinterest decimal, and the time in principal I ! Prt simple years. annual interest rate r written as a decimal, and the tim ! (100)(0.05)(1) Substitute 100 for P, 0.05 for r, and 1 for t. years. ! 5Algebra I ! Prt Multiply. To findNumbers the balance, the interest principal. A $500 earns to 6%the simple annual interest for Algebra Iadd !deposit Prt 4 years. I ! ($500)(0.06)(4) ! $120 ANSWER Tim will owe a balance of $100 " $5, or $105.
Numbers A $500 deposit earns 6% simple annual inter
4 years. I ! ($500)(0.06)(4) ! $120 EXAMPLE
1
Finding a Balance
To find the total amount that Tim will owe, as described above, first find the interest using the simple interest formula.
E X A IM!PPrt LE
1
! (100)(0.05)(1)
Write simple formula. Finding ainterest Balance Substitute 100 for P, 0.05 for r, and 1 for t.
principal . When amount of money deposited or borrowed is W the HY? Ininterest the isReal earnedWorld or paid only on the principal, it is simple interest . The u calculated discounts, You’ll calculate simple of the principal So you canearned find the amount of per a annual interest rate is the percent or paid arkups, sales tax, and tips. interest. security deposit, as in Ex. 19. year. The sum of the interest and thelend principal is called the balance . Family Loan Tim’s parents Tim
Now
EFORE
nts
$100 so he can buy a radio-controlled In airplane. the Real They Worldcharge Tim 5% simple annual interest. Whatlend will be the total Simple Interest Family Loan Tim’s parents Tim $100 so he can a radio-controlled amount thatbuy Tim will owe his parents Words Simple interest I is the product of the principal P, the airplane. They charge Tim 5% simple in 1annual year? interest rate r written as a decimal, and the time t in
annual interest. What will be the total years. amount that Tim will owe his parents The amount earned or paid for the use of money is called in in 1 year? Algebra I ! Prt amount of money deposited or borrowed is the principal . W The amount earned or paid for the use of money is called interest . The interest earned or paid only theprincipal principal, it for is simple i Numbers A $500 deposit 6%on simple annual interest amount of is money deposited or earns borrowed is the . When 4 years. I ! ($500)(0.06)(4) !the $120 annual rateonlyison the percent principal o simple interest earned interest is interest earned or paid principal,of it isthe . The annual interest rate the interest percent of and the principal earned or is paid per the b year. The sum ofisthe the principal called year. The sum of the interest and the principal is called the balance .
EXAMPLE
1
Finding a Balance
Simple Interest Simple Interest
To find the total amount that Tim will owe, as described above, first find the interest theinterest simple Iinterest formula. Wordsusing Simple is the product of the principal P, the Words Simple is theformula. product of tthe annual interest rateWrite r interest written as aIinterest decimal, and the time in principal I ! Prt simple years. annual interest rate r written as a decimal, and the tim ! (100)(0.05)(1) Substitute 100 for P, 0.05 for r, and 1 for t. years. ! 5Algebra I ! Prt Multiply. To findNumbers the balance, the interest principal. A $500 earns to 6%the simple annual interest for Algebra Iadd !deposit Prt 4 years. I ! ($500)(0.06)(4) ! $120 ANSWER Tim will owe a balance of $100 " $5, or $105.
Numbers A $500 deposit earns 6% simple annual inter
4 years. I ! ($500)(0.06)(4) ! $120 EXAMPLE
1
Finding a Balance
To find the total amount that Tim will owe, as described above, first find the interest using the simple interest formula.
E X A IM!PPrt LE
1
! (100)(0.05)(1)
Write simple formula. Finding ainterest Balance Substitute 100 for P, 0.05 for r, and 1 for t.
principal . When amount of money deposited or borrowed is W the HY? Ininterest the isReal earnedWorld or paid only on the principal, it is simple interest . The u calculated discounts, You’ll calculate simple of the principal So you canearned find the amount of per a annual interest rate is the percent or paid arkups, sales tax, and tips. interest. security deposit, as in Ex. 19. year. The sum of the interest and thelend principal is called the balance . Family Loan Tim’s parents Tim
Now
EFORE
nts
$100 so he can buy a radio-controlled In airplane. the Real They Worldcharge Tim 5% simple annual interest. Whatlend will be the total Simple Interest Family Loan Tim’s parents Tim $100 so he can a radio-controlled amount thatbuy Tim will owe his parents Words Simple interest I is the product of the principal P, the airplane. They charge Tim 5% simple in 1annual year? interest rate r written as a decimal, and the time t in
annual interest. What will be the total years. amount that Tim will owe his parents The amount earned or paid for the use of money is called in in 1 year? Algebra I ! Prt amount of money deposited or borrowed is the principal . W The amount earned or paid for the use of money is called interest . The interest earned or paid only theprincipal principal, it for is simple i Numbers A $500 deposit 6%on simple annual interest amount of is money deposited or earns borrowed is the . When 4 years. I ! ($500)(0.06)(4) !the $120 annual rateonlyison the percent principal o simple interest earned interest is interest earned or paid principal,of it isthe . The annual interest rate the interest percent of and the principal earned or is paid per the b year. The sum ofisthe the principal called year. The sum of the interest and the principal is called the balance .
EXAMPLE
1
Finding a Balance
Simple Interest Simple Interest
To find the total amount that Tim will owe, as described above, first find the interest theinterest simple Iinterest formula. Wordsusing Simple is the product of the principal P, the Words Simple is theformula. product of tthe annual interest rateWrite r interest written as aIinterest decimal, and the time in principal I ! Prt simple years. annual interest rate r written as a decimal, and the tim ! (100)(0.05)(1) Substitute 100 for P, 0.05 for r, and 1 for t. years. ! 5Algebra I ! Prt Multiply. To findNumbers the balance, the interest principal. A $500 earns to 6%the simple annual interest for Algebra Iadd !deposit Prt 4 years. I ! ($500)(0.06)(4) ! $120 ANSWER Tim will owe a balance of $100 " $5, or $105.
Numbers A $500 deposit earns 6% simple annual inter
4 years. I ! ($500)(0.06)(4) ! $120 EXAMPLE
1
Finding a Balance
To find the total amount that Tim will owe, as described above, first find the interest using the simple interest formula.
E X A IM!PPrt LE
1
! (100)(0.05)(1)
Write simple formula. Finding ainterest Balance Substitute 100 for P, 0.05 for r, and 1 for t.
principal . When amount of money deposited or borrowed is W the HY? Ininterest the isReal earnedWorld or paid only on the principal, it is simple interest . The u calculated discounts, You’ll calculate simple of the principal So you canearned find the amount of per a annual interest rate is the percent or paid arkups, sales tax, and tips. interest. security deposit, as in Ex. 19. year. The sum of the interest and thelend principal is called the balance . Family Loan Tim’s parents Tim
Now
EFORE
nts
$100 so he can buy a radio-controlled In airplane. the Real They Worldcharge Tim 5% simple annual interest. Whatlend will be the total Simple Interest Family Loan Tim’s parents Tim $100 so he can a radio-controlled amount thatbuy Tim will owe his parents Words Simple interest I is the product of the principal P, the airplane. They charge Tim 5% simple in 1annual year? interest rate r written as a decimal, and the time t in
annual interest. What will be the total years. amount that Tim will owe his parents The amount earned or paid for the use of money is called in in 1 year? Algebra I ! Prt amount of money deposited or borrowed is the principal . W The amount earned or paid for the use of money is called interest . The interest earned or paid only theprincipal principal, it for is simple i Numbers A $500 deposit 6%on simple annual interest amount of is money deposited or earns borrowed is the . When 4 years. I ! ($500)(0.06)(4) !the $120 annual rateonlyison the percent principal o simple interest earned interest is interest earned or paid principal,of it isthe . The annual interest rate the interest percent of and the principal earned or is paid per the b year. The sum ofisthe the principal called year. The sum of the interest and the principal is called the balance .
EXAMPLE
1
Finding a Balance
Simple Interest Simple Interest
To find the total amount that Tim will owe, as described above, first find the interest theinterest simple Iinterest formula. Wordsusing Simple is the product of the principal P, the Words Simple is theformula. product of tthe annual interest rateWrite r interest written as aIinterest decimal, and the time in principal I ! Prt simple years. annual interest rate r written as a decimal, and the tim ! (100)(0.05)(1) Substitute 100 for P, 0.05 for r, and 1 for t. years. ! 5Algebra I ! Prt Multiply. To findNumbers the balance, the interest principal. A $500 earns to 6%the simple annual interest for Algebra Iadd !deposit Prt 4 years. I ! ($500)(0.06)(4) ! $120 ANSWER Tim will owe a balance of $100 " $5, or $105.
Numbers A $500 deposit earns 6% simple annual inter
4 years. I ! ($500)(0.06)(4) ! $120 EXAMPLE
1
Finding a Balance
To find the total amount that Tim will owe, as described above, first find the interest using the simple interest formula.
E X A IM!PPrt LE
1
! (100)(0.05)(1)
Write simple formula. Finding ainterest Balance Substitute 100 for P, 0.05 for r, and 1 for t.
principal . When amount of money deposited or borrowed is W the HY? Ininterest the isReal earnedWorld or paid only on the principal, it is simple interest . The u calculated discounts, You’ll calculate simple of the principal So you canearned find the amount of per a annual interest rate is the percent or paid arkups, sales tax, and tips. interest. security deposit, as in Ex. 19. year. The sum of the interest and thelend principal is called the balance . Family Loan Tim’s parents Tim
Now
EFORE
nts
$100 so he can buy a radio-controlled In airplane. the Real They Worldcharge Tim 5% simple annual interest. Whatlend will be the total Simple Interest Family Loan Tim’s parents Tim $100 so he can a radio-controlled amount thatbuy Tim will owe his parents Words Simple interest I is the product of the principal P, the airplane. They charge Tim 5% simple in 1annual year? interest rate r written as a decimal, and the time t in
annual interest. What will be the total years. amount that Tim will owe his parents The amount earned or paid for the use of money is called in in 1 year? Algebra I ! Prt amount of money deposited or borrowed is the principal . W The amount earned or paid for the use of money is called interest . The interest earned or paid only theprincipal principal, it for is simple i Numbers A $500 deposit 6%on simple annual interest amount of is money deposited or earns borrowed is the . When 4 years. I ! ($500)(0.06)(4) !the $120 annual rateonlyison the percent principal o simple interest earned interest is interest earned or paid principal,of it isthe . The annual interest rate the interest percent of and the principal earned or is paid per the b year. The sum ofisthe the principal called year. The sum of the interest and the principal is called the balance .
EXAMPLE
1
Finding a Balance
Simple Interest Simple Interest
To find the total amount that Tim will owe, as described above, first find the interest theinterest simple Iinterest formula. Wordsusing Simple is the product of the principal P, the Words Simple is theformula. product of tthe annual interest rateWrite r interest written as aIinterest decimal, and the time in principal I ! Prt simple years. annual interest rate r written as a decimal, and the tim ! (100)(0.05)(1) Substitute 100 for P, 0.05 for r, and 1 for t. years. ! 5Algebra I ! Prt Multiply. To findNumbers the balance, the interest principal. A $500 earns to 6%the simple annual interest for Algebra Iadd !deposit Prt 4 years. I ! ($500)(0.06)(4) ! $120 ANSWER Tim will owe a balance of $100 " $5, or $105.
Numbers A $500 deposit earns 6% simple annual inter
4 years. I ! ($500)(0.06)(4) ! $120 EXAMPLE
1
Finding a Balance
To find the total amount that Tim will owe, as described above, first find the interest using the simple interest formula.
E X A IM!PPrt LE
1
! (100)(0.05)(1)
Write simple formula. Finding ainterest Balance Substitute 100 for P, 0.05 for r, and 1 for t.
principal . When amount of money deposited or borrowed is W the HY? Ininterest the isReal earnedWorld or paid only on the principal, it is simple interest . The u calculated discounts, You’ll calculate simple of the principal So you canearned find the amount of per a annual interest rate is the percent or paid arkups, sales tax, and tips. interest. security deposit, as in Ex. 19. year. The sum of the interest and thelend principal is called the balance . Family Loan Tim’s parents Tim
Now
EFORE
nts
$100 so he can buy a radio-controlled In airplane. the Real They Worldcharge Tim 5% simple annual interest. Whatlend will be the total Simple Interest Family Loan Tim’s parents Tim $100 so he can a radio-controlled amount thatbuy Tim will owe his parents Words Simple interest I is the product of the principal P, the airplane. They charge Tim 5% simple in 1annual year? interest rate r written as a decimal, and the time t in
annual interest. What will be the total years. amount that Tim will owe his parents The amount earned or paid for the use of money is called in in 1 year? Algebra I ! Prt amount of money deposited or borrowed is the principal . W The amount earned or paid for the use of money is called interest . The interest earned or paid only theprincipal principal, it for is simple i Numbers A $500 deposit 6%on simple annual interest amount of is money deposited or earns borrowed is the . When 4 years. I ! ($500)(0.06)(4) !the $120 annual rateonlyison the percent principal o simple interest earned interest is interest earned or paid principal,of it isthe . The annual interest rate the interest percent of and the principal earned or is paid per the b year. The sum ofisthe the principal called year. The sum of the interest and the principal is called the balance .
EXAMPLE
1
Finding a Balance
Simple Interest Simple Interest
To find the total amount that Tim will owe, as described above, first find the interest theinterest simple Iinterest formula. Wordsusing Simple is the product of the principal P, the Words Simple is theformula. product of tthe annual interest rateWrite r interest written as aIinterest decimal, and the time in principal I ! Prt simple years. annual interest rate r written as a decimal, and the tim ! (100)(0.05)(1) Substitute 100 for P, 0.05 for r, and 1 for t. years. ! 5Algebra I ! Prt Multiply. To findNumbers the balance, the interest principal. A $500 earns to 6%the simple annual interest for Algebra Iadd !deposit Prt 4 years. I ! ($500)(0.06)(4) ! $120 ANSWER Tim will owe a balance of $100 " $5, or $105.
Numbers A $500 deposit earns 6% simple annual inter
4 years. I ! ($500)(0.06)(4) ! $120 EXAMPLE
1
Finding a Balance
To find the total amount that Tim will owe, as described above, first find the interest using the simple interest formula.
E X A IM!PPrt LE
1
! (100)(0.05)(1)
Write simple formula. Finding ainterest Balance Substitute 100 for P, 0.05 for r, and 1 for t.
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
EXAMPLE
2
Finding an Interest Rate
You deposit $600 into a 6 month certificate of deposit. After 6 months the balance is $618. Find the simple annual interest rate. 1 To find the interest, subtract the principal from the balance. $618 ! $600 " $18 2 Use the simple interest formula and solve for r. I " Prt
Write simple interest formula.
! " 6 12
6 12
18 " (600)(r) ##
Substitute 18 for I, 600 for P, and ## for t.
18 " 300r
Multiply.
18 300r ## " ## 300 300
Divide each side by 300.
0.06 " r
Simplify.
6% " r
Write decimal as a percent.
ANSWER The simple annual interest rate is 6%.
Your turn now
Solve the following problems.
1. If you deposit $500 into an account that earns 6% simple annual
interest, what will the account’s balance be after 10 months? 2. You deposit $1000 into a 3 month certificate of deposit. After
3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual
2. You deposit $1000 into a 3 month certificate of deposit. After 3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual interest rate is 4%. You receive a check for the interest at the end of each year. How long will it take to earn $150 in interest? I " Prt
Write simple interest formula.
150 " (750)(0.04)t
Substitute 150 for I, 750 for P, and 0.04 for r.
150 " 30t
Multiply.
150 30t ## " ## 30 30
Divide each side by 30.
5"t
Simplify.
ANSWER It will take 5 years to earn $150 in interest.
Lesson 9.8
Simple Interest
455
2. You deposit $1000 into a 3 month certificate of deposit. After 3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual interest rate is 4%. You receive a check for the interest at the end of each year. How long will it take to earn $150 in interest? I " Prt
Write simple interest formula.
150 " (750)(0.04)t
Substitute 150 for I, 750 for P, and 0.04 for r.
150 " 30t
Multiply.
150 30t ## " ## 30 30
Divide each side by 30.
5"t
Simplify.
ANSWER It will take 5 years to earn $150 in interest.
Lesson 9.8
Simple Interest
455
2. You deposit $1000 into a 3 month certificate of deposit. After 3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual interest rate is 4%. You receive a check for the interest at the end of each year. How long will it take to earn $150 in interest? I " Prt
Write simple interest formula.
150 " (750)(0.04)t
Substitute 150 for I, 750 for P, and 0.04 for r.
150 " 30t
Multiply.
150 30t ## " ## 30 30
Divide each side by 30.
5"t
Simplify.
ANSWER It will take 5 years to earn $150 in interest.
Lesson 9.8
Simple Interest
455
2. You deposit $1000 into a 3 month certificate of deposit. After 3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual interest rate is 4%. You receive a check for the interest at the end of each year. How long will it take to earn $150 in interest? I " Prt
Write simple interest formula.
150 " (750)(0.04)t
Substitute 150 for I, 750 for P, and 0.04 for r.
150 " 30t
Multiply.
150 30t ## " ## 30 30
Divide each side by 30.
5"t
Simplify.
ANSWER It will take 5 years to earn $150 in interest.
Lesson 9.8
Simple Interest
455
2. You deposit $1000 into a 3 month certificate of deposit. After 3 months the balance is $1005. Find the simple annual interest rate.
EXAMPLE
3
Finding an Amount of Time
You put $750 into a certificate of deposit. Your simple annual interest rate is 4%. You receive a check for the interest at the end of each year. How long will it take to earn $150 in interest? I " Prt
Write simple interest formula.
150 " (750)(0.04)t
Substitute 150 for I, 750 for P, and 0.04 for r.
150 " 30t
Multiply.
150 30t ## " ## 30 30
Divide each side by 30.
5"t
Simplify.
ANSWER It will take 5 years to earn $150 in interest.
Lesson 9.8
Simple Interest
455
4. $50 at 10% for 4 years
5. $200 at 4.5% for 8 months
Use the simple interest formula to find the unknown quantity. 6. Investments You deposit $250 into a 6 month certificate of deposit. At 14. I ! _?_ 15. I ! $84 16. I ! $468 17. I ! $9 the end of the 6 months your balance is $255. What is the simple Pannual ! $2000 P ! _?_ P ! $6240 P ! $450 interest Answer each rate? ques-on in your notes r ! 9.8% r ! 7% r ! _?_ r ! 4% 7. tSavings Suppose you $750 into a savings account that tearns ! 5 years t !put 2 years t ! 9 months ! _?_
2% simple annual interest. How long will it take to have $45 in interest? 18. Writing If you borrow money, would you want a higher or lower
interest rate? If you open a savings account, would you want a higher Practice or a lower and interestProblem rate? Explain. Solving 21. Savings Deposit Suppose When Ann has $300 ainlease a savings that your earnssister 1.75% 19. signing for anaccount apartment, For Security an account that earns simple annual interest, find the interest simple annual interest. In how many willannual she have $21 inAtinterest? a security that earns 3.5%years simple interest. the andpays the balance of deposit the account. end of aCards year, the interest earned on 9.6% the security deposit ison $17.50. How 22. Credit credit card charges annual interest any unpaid 8. much $252 atwas 8%the for A 2security months 9. $450 at 4% for 6 months deposit? balance each month. During the past month your older brother had an 10. unpaid $6240 atbalance 10% for of 9 months $2000 atof9.6% for 8 months $375 from the11. purchase a computer desk. What is 20. Critical Thinking Three months ago you deposited $250 into a savings the interest for that month? 12. account, $5000 at 4.5% for 1 your year $400 at 3% for 1 month andcharge now balance is13. $253. Eight months ago your friend deposited $250 into a different savings account, and her balance is now 23. Challenge Suppose you put $500 in a savings account that earns 4.5% Use$257.50. the simple interest formula to find the simple unknown quantity. Which account has the greater annual interest rate?
simple annual interest, and your friend puts $400 in a savings account
14. that I ! _?earns _ 15. I ! annual $84 16. I ! $468 of you17. I! $9 $600 first? 6% simple interest. Which will earn
P ! $2000 r ! 9.8% t ! 5 years
Mixed Review
P ! _?_ r ! 7% t ! 2 years
P ! $6240 r ! _?_ t ! 9 months
P ! $450 r ! 4% t ! _?_
18. Writing If you borrow money, would you want a higher or lower
Solveinterest the equation. (Lesson rate? If you open a7.5) savings account, would you want a higher z or a lower interest rate? Explain. 24. 5x ! 4 " #21 25. #6 # 12y " #54 26. $$ # 8 " 3 7 19. Security Deposit When signing a lease for an apartment, your sister x $ ! 2a" 27. $pays 12 28. 5 earns " 3n # 4 simple annual 29. #2y # 8 "At#10 security deposit that 3.5% interest. the 5 end of a year, the interest earned on the security deposit is $17.50. How much was the security deposit?
Choose a Strategy Use a strategy from Problem Strategies 20. list Critical Thinking Three months ago you deposited $250Solving into a savings the to solve the following problem. Work ago Backward account, nowof your balance is $253. Eight months your friend Explain your and choice strategy. ■
■ Make a List deposited $250 into a different savings account, and her balance is now 30. Your friends Tom, Ryan, Jen, Matt, and Al ■ Act it Out $257.50. Which account has the greater simple annual interest rate?
line up in a row. Tom, Jen, and Ryan are not next to each other. Tom is at one end. Two people separate Jen and Matt. Between which two people is Al?
Basic Skills Copy and complete the statement using <, >, or !.
Compound Interest A = P(1 + r)t P = original amount deposited r = interest rate (percent as a decimal) t = time
,600 in an account that pays 4% interest compounded end of 7 years.
__
r = __________
t = ______
balance at the end of 7 years. r = interest rate (percent as a decimal)
nswer the question about the given investment. P = __________
r = __________ t = time
t = __________
7. What is theebalance after 8 years if youndeposit Answer ach ques-on in your otes $1400 in an account that pays 6% 3. You deposit $1,600 in anyearly? account that pays 4% interest compounded yearly. Find the interest compounded balance at the end of 7 years. P = __________
r = __________
t = __________
4. You deposit money in an account that pays 3.5% interest compounded yearly. Find the nswer the question about the given investment. balance after 5 years for an initial amount of $750. 7. What is the balance after 8 years if you deposit $1400 in an account that pays 6% compounded yearly? r = __________ Pinterest = __________ t = __________
4. deposit in after an account that paysdeposit 3.5% interest Find 8. You What is themoney balance 5 years if you $350 incompounded an account yearly. that pays 5%the inter balance after 5 years for an initial amount of $750.
compounded yearly? swer the question about the given investment. P = __________
r = __________
t = __________
7. What is the balance after 8 years if you deposit $1400 in an account that pays 6% interest compounded yearly? 5. You deposit $2,000 in an account that compounds interest yearly. Find the balance after 10 years for an interest rate of 6%. 8. What is the balance after 5 years if you deposit $350 in an account that pays 5% interest compounded yearly? P = __________ r = __________ t = __________ 5. You deposit $2,000 in an account that compounds interest yearly. Find the balance for an interest of 6%. 9. after What10isyears the balance after 10rate years if you deposit $900 in an account that pays 7%
interest compounded yearly? P = __________
r = __________
t = __________
8. What is the balance after 5 years if you deposit $350 in an account that pays 5% intere compounded yearly? 9. What is the balance after 10 years if you deposit $900 in an account that pays 7% interest compounded yearly?
To “compound” interest means adding the accumulated interest back to the original amount in the account. To “continuously compound” interest means adding interest every instant The Compound Interest Formula is A
r P 1 n
nt
A represents P represents r represents t represents n represents Let’s try some examples using the Compound Interest Formula…
1. Suppose Wes has $1000 that he invests in an account that pays 3.5% interest compounded quarterly. How much money does Wes have at the end of 5 years? How much interest will he earn?
n represents Letâ&#x20AC;&#x2122;s try some examples using the Compound Interest Formulaâ&#x20AC;Ś
1. Suppose Wes has $1000 that he invests in an account that pays 3.5% interest compounded quarterly. How much money does Wes have at the end of 5 years? How much interest will he earn?
n represents Letâ&#x20AC;&#x2122;s try some examples using the Compound Interest Formulaâ&#x20AC;Ś
1. Suppose Wes has $1000 that he invests in an account that pays 3.5% interest compounded quarterly. How much money does Wes have at the end of 5 years? How much interest will he earn?
n represents Letâ&#x20AC;&#x2122;s try some examples using the Compound Interest Formulaâ&#x20AC;Ś
1. Suppose Wes has $1000 that he invests in an account that pays 3.5% interest compounded quarterly. How much money does Wes have at the end of 5 years? How much interest will he earn?
n represents Letâ&#x20AC;&#x2122;s try some examples using the Compound Interest Formulaâ&#x20AC;Ś
1. Suppose Wes has $1000 that he invests in an account that pays 3.5% interest compounded quarterly. How much money does Wes have at the end of 5 years? How much interest will he earn?
n represents Letâ&#x20AC;&#x2122;s try some examples using the Compound Interest Formulaâ&#x20AC;Ś
1. Suppose Wes has $1000 that he invests in an account that pays 3.5% interest compounded quarterly. How much money does Wes have at the end of 5 years? How much interest will he earn?
Interest Word Problems A
r P 1 n
Date_________________
nt
2. William wants to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% interest compounded monthly. How much should William put into this account so that heâ&#x20AC;&#x2122;ll have $4000 at the end of two years?
3. Suppose William, from our last example, only has $3500 to invest but still wants $4000 for a hot tub. He finds a bank offering 5.25% interest compounded quarterly. How long will he have to leave his money in the account to have $4000?
Interest Word Problems A
r P 1 n
Date_________________
nt
2. William wants to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% interest compounded monthly. How much should William put into this account so that heâ&#x20AC;&#x2122;ll have $4000 at the end of two years?
3. Suppose William, from our last example, only has $3500 to invest but still wants $4000 for a hot tub. He finds a bank offering 5.25% interest compounded quarterly. How long will he have to leave his money in the account to have $4000?
Interest Word Problems A
r P 1 n
Date_________________
nt
2. William wants to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% interest compounded monthly. How much should William put into this account so that heâ&#x20AC;&#x2122;ll have $4000 at the end of two years?
3. Suppose William, from our last example, only has $3500 to invest but still wants $4000 for a hot tub. He finds a bank offering 5.25% interest compounded quarterly. How long will he have to leave his money in the account to have $4000?
Interest Word Problems A
r P 1 n
Date_________________
nt
2. William wants to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% interest compounded monthly. How much should William put into this account so that heâ&#x20AC;&#x2122;ll have $4000 at the end of two years?
3. Suppose William, from our last example, only has $3500 to invest but still wants $4000 for a hot tub. He finds a bank offering 5.25% interest compounded quarterly. How long will he have to leave his money in the account to have $4000?