Resources

Resources

Compound interest

Jeanne's bank account earns interest annually. The equation shows her starting balance of

\$ 350

and her balance at the end of three years,

\$ 422.78

. At what rate r did Jeanne earn interest?

\newline

422.78=350(1+r)^{3}

63

\cdot\left(-\dfrac{

1

3

}\right)^{\large{\,n}} Complete the recursive formula of

h(n)

-1

\newline

1

3

\newline

1

3

\newline

-3

\newline

3

63

\cdot\left(-\dfrac{

1

3

}\right)^{\large{\,n}} Complete the recursive formula of

h(n)

-1

\newline

1

3

\newline

1

3

\newline

-3

\newline

3

An investment of

\$1,200

is made in an account with continuous compounding. After

8

years, the account balance is

\$2,400

. Determine the annual interest rate. Round your answer to the nearest two decimal places in percentage form. Use the formula

A = Pe^{rt}

A

is the balance (final amount),

P

is the principal (starting amount),

e

is the base of natural logarithms (

\approx 2.71828

r

is the interest rate expressed as a decimal, and

t

is the time in years.

An initial investment of

\$3,000

\$9,000

over a period of

5

years in an account with continuous compounding. What is the annual interest rate? Round your answer to the nearest two decimal places in percentage form. Use the formula

A = Pe^{rt}

A

is the balance (final amount),

P

is the principal (starting amount),

e

is the base of natural logarithms (

\approx 2.71828

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\$8,000

in a savings account. After

10

years, her investment grew to

\$12,000

. What is the annual interest rate, compounded continuously, that Sarah's account earned? Round your answer to the nearest two decimal places in percentage form. Use the formula

A = Pe^{rt}

A

is the balance (final amount),

P

is the principal (starting amount),

e

is the base of natural logarithms (

\approx 2.71828

r

is the interest rate expressed as a decimal, and

t

is the time in years.

An art collector invested

\$40,000

in a trust fund with a

5.9\%

interest rate compounded continuously to save for future art acquisitions. How long will it take for the trust fund to grow to

\$80,000

?

\newline

Use the formula

A = Pe^{rt}

A

is the balance (final amount),

P

is the principal (starting amount),

e

is the base of natural logarithms

(\approx 2.71828)

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\newline

Round your answer to the nearest tenth.

The country of Freedonia has decided to reduce its carbon-dioxide emission by

35 ext{ ext{\%}}

each year. This year the country emitted

40

million tons of carbon-dioxide. Write a function that gives Freedonia's carbon-dioxide emissions in million tons,

E(t)

t

years from today.

\$50000

from a bank at an interest rate of

24

\% p.a., compounded monthly. H repays the bank

\$3000

at the end of each month after the interest is calculated. How much doe he still owe the bank just after his second repayment?

\newline

\$34698

\newline

\$39658

\newline

50000 \times (1+\frac{24}{12})^{7-x}

\newline

\$39900

\newline

\$45960

\$50000

from a bank at an interest rate of

24

\% p.a., compounded monthly. H repays the bank

\$3000

at the end of each month after the interest is calculated. How much doe he still owe the bank just after his second repayment?

\newline

\$34698

\newline

\$39658

\newline

50000 \times (1+\frac{24}{12})^{7-x}

\newline

\$39900

\newline

\$45960

20

\$

in an account that earns

5\%

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

1

year? 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.

\$

Evelyn deposited

90

\$

in an account earning

10\%

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

1

year? 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.

\$

20

\$

in an account. The interest rate is

10\%

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

1

year? 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.

\$

70

\$

in an account. The interest rate is

5\%

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

1

year? 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.

\$

Valeria deposited

80

\$

in an account earning

5\%

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

\$

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

6.3\%

compounded monthly. If Sophia would like to end up with

\$65,000

11

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$2000

from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money.

\newline

The relationship between the amount of money,

A

, in dollars that Noah owes his father (including interest), and the elapsed time,

t

, in years, is modeled by the following equation.

\newline

A=2000e^{0.1t}

\newline

How long did it take Noah to pay off his loan if the amount he paid to his father was equal to

\$2450

\newline

Give an exact answer expressed as a natural logarithm.

\newline

\square

Ms. Donose decided to put

\$ 1500

into a savings account that earns

2.5 \%

interest compounded semi-annually. Using the equation

A=P\left(1+\frac{r}{n}\right)^{n t}

, find out how much money she will have after

29

\$ 3,582

in an account that earns

5 \%

interest compounded annually.

\newline

To the nearest cent, how much will he have in

1

\newline

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.

\newline

\$

\square

The following formula gives the volume

V

of a pyramid, where

A

is the area of the base and

h

\newline

V=\frac{1}{3} A h

\newline

Rearrange the formula to highlight the base area.

\newline

A=

Kadeesha invests money in an account paying a simple interest of

2 \%

per year. If no money will be added or removed from the investment, what should she multiply her current balance by to find her total balance in a year in one step?

\newline

Ella invests money in an account paying a simple interest of

5.2 \%

m

represents the amount of money she invests, which expression does NOT represent her balance after a year, assuming she makes no additional withdrawals or deposits?

\newline

1.0052 m

\newline

1.052 m

\newline

(1+0.052) m

\newline

1 m+0.052 m

Andres invests money in an account paying a simple interest of

6.8 \%

m

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

\newline

1+0.068

\newline

1.0068 m

\newline

1.068 m

\newline

1+0.068 m

Deondra has a loyalty card good for a

11 \%

discount at her local grocery store. If the total cost, before tax and discount, of all the items she wants to buy is

c

, which expression does NOT represent the cost after the discount?

\newline

(1-0.11) c

\newline

c-0.11 c

\newline

11 c

\newline

1 c-0.11 c

The present value

PV

of an investment is the amount that should be invested today at a specified interest rate in order to earn a certain amount at a future date. The amount desired is called the future value. For a future value of

\$10,000

, which of the following functions models the present value,

PV

, to be invested in a savings account earning

5\%

interest compounded annually for

t

Arianna deposits

\$ 450

every month into an account earning a monthly interest rate of

0.525 \%

. How much would she have in the account after

24

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 750

every month into an account earning a monthly interest rate of

0.4 \%

. How much would she have in the account after

3

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Madeline deposits

\$ 5,800

every year into an account earning an annual interest rate of

5.2 \%

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

15

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 7,500

every year into an account earning an annual interest rate of

5.9 \%

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

10

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 830

every month into an account earning an annual interest rate of

3.9 \%

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

9

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Savannah deposits

\$ 360

every month into an account earning a monthly interest rate of

0.65 \%

. How much would she have in the account after

8

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Mackenzie deposits

\$ 690

every month into an account earning a monthly interest rate of

0.25 \%

. How much would she have in the account after

13

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 8,700

every year into an account earning an annual interest rate of

7.9 \%

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

14

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 290

every month into an account earning a monthly interest rate of

0.7 \%

. How much would he have in the account after

13

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Natalie deposits

\$ 320

every month into an account earning an annual interest rate of

9 \%

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

4

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Miguel deposits

\$ 470

every month into an account earning an annual interest rate of

8.1 \%

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

30

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 380

every month into an account earning a monthly interest rate of

0.35 \%

. How much would he have in the account after

7

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 560

every quarter into an account earning an annual interest rate of

8 \%

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.

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

\$ 880

every month into an account earning a monthly interest rate of

0.675 \%

. How much would he have in the account after

6

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Joseph is saving money and plans on making monthly contributions into an account earning a monthly interest rate of

0.75 \%

. If Joseph would like to end up with

\$ 259,000

13

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

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

1.875 \%

. If Josue would like to end up with

\$ 95,000

15

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

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

6.3 \%

compounded monthly. If Sophia would like to end up with

\$ 65,000

11

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

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

6.7 \%

compounded quarterly. If Tanisha would like to end up with

\$ 96,000

11

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.

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

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

4.2 \%

compounded monthly. If Zachary would like to end up with

\$ 8,000

21

months, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

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

3.8 \%

compounded quarterly. If Audrey would like to end up with

\$ 6,000

8

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.

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Mohal is saving money and plans on making monthly contributions into an account earning a monthly interest rate of

0.45 \%

. If Mohal would like to end up with

\$ 19,000

30

months, how much does he need to contribute to the account every month, to the nearest dollar? Use the following formula to determine your answer.

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Aubree is saving money and plans on making monthly contributions into an account earning a monthly interest rate of

0.675 \%

. If Aubree would like to end up with

\$ 7,000

2

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Josiah is saving money and plans on making monthly contributions into an account earning a monthly interest rate of

0.35 \%

. If Josiah would like to end up with

\$ 12,000

5

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

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

0.475 \%

. If Emma would like to end up with

\$ 14,000

14

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline

Emily is saving money and plans on making monthly contributions into an account earning a monthly interest rate of

0.375 \%

. If Emily would like to end up with

\$ 4,000

13

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

\newline

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

\newline

A=

the future value of the account after

n

\newline

d=

the amount invested at the end of each period

\newline

i=

the interest rate per period

\newline

n=

the number of periods

\newline