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Compound interest

Select the correct answer.

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Taylor wants to purchase a car with an auto loan. He can get a

48

-month loan from his bank that is compounded monthly at an annual interest rate of

7.9\%

. Suppose Taylor needs to obtain a loan for $

19

076

to purchase the car. Use the formula for the sum of a finite geometric series to determine Taylor's approximate monthly payment.

P=\frac{B,(0)}{1-(1+0)^{-48}}

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A). Taylor's approximate monthly payment for the loan will be

\$

458

35

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B). Taylor's approximate monthly payment for the loan will be

\$

464

81

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C). Taylor's approximate monthly payment for the loan will be

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\$

546

50

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D). Taylor's approximate monthly payment for the loan will be

\$

4132

How much must be deposited today into the following account in order to have

\$50,000

7

years for a down payment on a house? Assume no additional deposits are made. An account with monthly compounding and an APR of

6\%

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\$

\square

should be deposited today.

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(Do not round until the final answer. Then round to the nearest cent as needed.)

Emmett deposited

90

\$

in an account earning

5\%

interest compounded annually. To the nearest cent, how much will he have in

2

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

80

\$

in an account. The interest rate is

5\%

compounded annually. To the nearest cent, how much will he have in

3

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

Tiana deposited

60

\$

in an account earning

10\%

interest compounded annually. To the nearest cent, how much will she have in

3

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

10

\$

in an account that earns

5\%

interest compounded annually. To the nearest cent, how much will she have in

2

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

30

\$

in an account earning

10\%

interest compounded annually. To the nearest cent, how much interest will she earn in

3

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

Tammy deposited

20

\$

in an account earning

10\%

interest compounded annually. To the nearest cent, how much interest will she earn in

3

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

50

\$

in an account that earns

5\%

interest compounded annually. To the nearest cent, how much interest will he earn in

3

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

90

\$

in an account. The interest rate is

5\%

compounded annually. To the nearest cent, how much will she have in

3

years? Use the formula

B = p(1 + r)^t

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$

Use the compound interest formula to compute the total amount accumulated and the interest earned.

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\$5000

4

3.8\%

compounded monthly.

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The total amount accumulated after

4

\$

\square

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(Round to the nearest cent as needed.)

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The amount of interest earned is

\$

\square

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(Round to the nearest cent as needed.)

\$ 15,000

is invested and at the end of

3 \mathrm{yr}

, the value of the account is

\$ 19,356.92

. Use the model

A=P e^{r t}

to determine the average rate of return

r

under continuous compounding.

\$ 10,000

is invested and at the end of

5

years, the value of the account is

\$ 13,771.28

. Use the model

A=P e^{r t}

to determine the average rate of return

r

under continuous compounding.

A loan grows to

\$ 3740

1

\$ 4114

2

years with compound interest which is computed annually. Find

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(a) the interest rate per annum,

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(b) the original loan.

Assuming your initial investment was made when you were

15

years old, how old would you be to have

\$ 1,000,000

in this account?

Calculate the future value of an ordinary annuity consisting of monthly payments of

\$470

for five years. The rate of return was

9.3\%

compounded monthly for the first two years, and will be

7.2\%

compounded monthly for the last three years. (Do not round intermediate calculations and round your final answer to

2

decimal places.) Future value

\$ 360

in an account that pays

1.2 \%

simple annual interest. How much interest will she earn in

6

Joseph invests money in an account paying a simple interest of

9 \%

m

represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?

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1.009 m

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0.09 m

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1.09 m

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9 m

Marques invests money in an account paying a simple interest of

8 \%

m

represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?

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0.08 m

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1.08 m

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8 m

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1.008 m

David invests money in an account paying a simple interest of

5.8 \%

m

represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?

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m+0.058

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1.0058 m

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1.058 m

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5.8 m

\$ 100

in an account. The interest rate is

6 \%

compounded annually.

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To the nearest cent, how much will he have in

2

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Use the formula

B=p(1+r)^{t}

B

is the balance (final amount),

p

is the principal (starting amount),

r

is the interest rate expressed as a decimal, and

t

is the time in years.

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\$

\square

The first year of a charity walk event had an attendance of

500

. The attendance

y

5 \%

each year. How many people will attend in the

10

th year? Round your answer to the nearest person.

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An account has a rate of

3.8\%

. Find the effective annual yield if the interest is compounded semiannually.

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The effective annual yield is

\square\%

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(Round to the nearest hundredth as needed.)

Dianelys deposits

\$ 6,100

every year into an account earning an annual interest rate of

5 \%

compounded annually. How much would she have in the account after

4

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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\$ 100

every quarter into an account earning a quarterly interest rate of

0.825 \%

. How much would he have in the account after

11

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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\$ 620

every year into an account earning an annual interest rate of

3.6 \%

compounded annually. How much would she have in the account after

9

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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\$ 910

every month into an account earning an annual interest rate of

3.9 \%

compounded monthly. How much would she have in the account after

13

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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Emma is saving money and plans on making annual contributions into an account earning an annual interest rate of

8

\% compounded annually. If Emma would like to end up with

\$ 18,000

15

years, how much does she need to contribute to the account every year, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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\$ 5,800

every year into an account earning an annual interest rate of

6.8 \%

compounded annually. How much would he have in the account after

6

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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\$ 490

every year into an account earning an annual interest rate of

5.3 \%

compounded annually. How much would he have in the account after

3

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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\$ 1,900

every quarter into an account earning an annual interest rate of

5.5 \%

compounded quarterly. How much would she have in the account after

12

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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Abdoulaye deposits

\$ 310

every month into an account earning a monthly interest rate of

0.475 \%

. How much would he have in the account after

6

months, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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\$ 4,200

every year into an account earning an annual interest rate of

8.1 \%

compounded annually. How much would she have in the account after

3

years, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

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A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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Mariam is saving money and plans on making quarterly contributions into an account earning an annual interest rate of

5 \%

compounded quarterly. If Mariam would like to end up with

\$ 8,000

3

years, how much does she need to contribute to the account every quarter, to the nearest dollar? Use the following formula to determine your answer.

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A=d\left(\frac{(1+i)^{n}-1}{i}\right)

\newline

A=

the future value of the account after

n

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d=

the amount invested at the end of each period

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i=

the interest rate per period

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n=

the number of periods

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Brianna invested

\$ 800

in an account that pays

2 \%

interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Brianna would have in the account

15

years after her initial investment. Round your answer to the nearest whole number.

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\$

\square

Kehlani bought stock in a company two years ago that was worth

x

dollars. During the first year that she owned the stock, it increased by

28 \%

. During the second year the value of the stock increased by

26 \%

. Write an expression in terms of

x

that represents the value of the stock after the two years have passed.

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\$ 4,848

in a savings account with a fixed annual interest rate of

5 \%

2

times per year. What will the account balance be after

6

7

900

dollars is placed in a savings account with an annual interest rate of

6 \%

. If no money is added or removed from the account, which equation represents how much will be in the account after

6

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M=7,900(1.06)^{6}

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M=7,900(0.06)^{6}

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M=7,900(1+0.06)(1+0.06)(1+0.06)

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M=7,900(1-0.06)^{6}

7

900

dollars is placed in a savings account with an annual interest rate of

3 \%

. If no money is added or removed from the account, which equation represents how much will be in the account after

5

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M=7,900(1.3)^{5}

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M=7,900(1-0.03)^{5}

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M=7,900(0.97)^{5}

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M=7,900(1.03)^{5}

\$2000

in a certificate of deposit that earns

2\%

in interest each year. Write a function that gives the total value

V(t)

, in dollars, of the investment

t

years from now.

Donald Rivera purchased a leather living room set for

\$4750

\$500

down. The balance was financed for

21

equal monthly payments, and Donald agreed to pay a

\$496

finance charge. Using the annual percentage rate (APR) table, calculate the following. (Round all answers to the nearest hundredth.)

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Amount financed:

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Annual percentage rate (APR):