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Interest Practice Problems

Interest Practice Problems

Use Excel to solve each problem. Try to do both the mathematical formula as well as the Excel function to check yourself.

Problem 1:

$3,000 is invested at 7.2% interest. Find the total amount (A) at the end of 5 years if:

a.) Simple interest is earned.

P=

$

i=

7.20%

n=

I=

A=

5

$

1,080.00

$

4,080.00

b.) Interest is compounded annually

P=

$

7.20%

n=

5

$

4,247.13

c.) Interest is compounded quarterly

P=

$

i=

20

$

4,286.24

d.) Interest is compounded monthly

P=

$

i=

3,000.00

0.60%

n=

A=

(see the "Other Compounding Periods" tab)

3,000.00

1.80%

n=

A=

(see the "Compound Interest Illustration" tab)

3,000.00

i=

A=

(see the "Simple Interest Example" tab)

3,000.00

60

$

4,295.37

(see the "Other Compounding Periods" tab)

Problem 2:

A department store charges 12% interest on the unpaid balance of customer charge accounts.

A customer owes $135, and the bill goes unpaid for 4 months. How much will the customer have to

repay after 4 months? Interest is compounded monthly (note that the 12% is an annual rate).

P=

$

i=

(see the "Other Compounding Periods" tab)

135.00

1.00%

n=

4 <---note that there are only 4 compounding periods, so n = 4

A=

$

140.48

Problem 3:

A typical family of four spends approximately $600 per month for food. Food costs are

predicted to rise by 4.8% per year for the next 5 years. In five years, how much should

the family budget per month for food? Treat this as compound annual growth.

(see the "Compound Interest Illustration" tab)

(assume annual compounding)

P=

$

i=

600.00

4.80%

n=

5

A=

$

758.50

Problem 4a:

A couple plans to begin saving money for a down payment toward the purchase of a home.

They plan to purchase a home 4 years from now. Right now, home prices are predicted

to rise by 5% per year for the next 5 years. If this prediction is accurate, how much

can this couple expect to pay in 4 years for a home that is currently valued at $210,000?

(what will be the total sales price in 4 years of a home worth $210,000 today?)

(use annual compounding)

P=

$

i=

5.00%

n=

A=

210,000.00

4

$

255,256.31

(see the "Compound Interest Illustration" tab)

Problem 4b:

The couple wants to have a 20% down payment on the purchase price in 4 years. Suppose they

have found a mutual fund that earns an average of 8% per year. How much should they invest in the

mutual fund today in order to have enough for a down payment in 4 years?

Assume annual compounding.

(Find the down payment first - that will be their "A" or future value of what they will invest)

(see the "Other Problem Types" tab - we are trying to find the principal or present value to be invested to grow to the down payment amount)

They want 20% of $255,256.31 as a down payment in 4 years.

A=

$

51,051.26

i=

8.00%

n=

4

P=

Problem 5:

$37,524.20

An electric company predicts that the cost of electricity will rise at the rate of 2% per

year for the next ten years. If the average monthly electricity for consumers in this area

is $225, predict the monthly amount that consumers can expect to pay 10 years from now.

(see the "Compound Interest Illustration" tab)

P=

$

225.00

i=

2.00%

n=

10

A=

$

274.27

Problem 6:

The managers of a retirement fund decided to invest $2.1 million in U.S. government

certificates of deposit that accumulate interest at the rate of 8.5% per year compounded

semiannually for the next 15 years. At the end of 15 years, how much will the investment be worth?

(see the "Other Compounding Periods" tab)

P=

$

i=

4.25%

n=

A=

2,100,000.00

30

$

7,319,833.53

Problem 7:

A couple established a trust fund for their son when he was born. They began with a

single deposit of $15,000 in the fund and the money will become available when their son

is 21 years old. How much will be in the account when he is 21 years old if interest is

8% per year compounded monthly?

(see the "Other Compounding Periods" tab)

P=

$

15,000.00

i=

0.67%

n=

252

A=

$

80,035.87

Problem 8:

How much money should be deposited today in a bank paying interest at the rate of 5.5% per

year compounded quarterly so that at the end of 5 years the accumulated amount will be

$2500?

(see the "Other Problem Types" tab)

A=

$

i=

1.38%

n=

20

P=

Problem 9:

2,500.00

$1,902.49

An individual purchased a 4-year, $20,000 promissory note with an interest rate of 7.5%

per year compounded semiannually (so the individual will receive $20,000 after four years).

What did this individual have to pay for this investment? (Find the principal if $20,000 will

be paid back four years in the future).

(see the "Other Problem Types" tab)

A=

$

20,000.00

i=

3.75%

n=

8

P=

$14,897.90

Problem 10:

A couple recently received a large inheritance and wish to invest this money in their child's

college education. After researching future predictions of college expenses, they agree that

they would like to have $100,000 available in 15 years. How much of the inheritance should

they set aside in a trust fund now if they can invest the money at 8 1/2% per year compounded

annaully? Compounded semiannually? Compounded quarterly? Compounded monthly?

(see the "Other Problem Types" tab)

A=

$

i=

8.50%

n=

15

P=

A=

$29,413.99

$

i=

100,000.00

30

P=

$28,689.18

$

2.13%

n=

60

P=

$28,318.86

$

with quarterly compounding

100,000.00

i=

0.71%

n=

180

P=

with semiannual compounding

100,000.00

i=

A=

with annual compounding

4.25%

n=

A=

100,000.00

$28,068.97

with monthly compounding

Problem 11:

A person invested a sum of money 8 years ago in a savings account that has since paid interest

at the rate of 5% per year compounded quarterly. His investment is now worth $22,289.22.

What was the amount of the original investment? (hint: treat the $22,289.22 as the future value, since

this was the future in terms of his original investment; the original investment is the present value or P)

(see the "Other Problem Types" tab)

A=

$

22,289.22

i=

1.25%

n=

32

P=

$14,978.00

Problem 12:

Find the effective rate of interest corresponding to a nominal rate of 9% per year when

compounded annually, semiannually, quarterly, and monthly. Round the percentages to the

hundredths place.

(see the "Other Problem Types" tab)

eff = (1+i)^m-1

Note that i = (annual rate)/(number of compounding periods)

Annual

i=

Semiannual

OR

Problem 13:

Monthly

9.00%

4.50%

2.25%

0.75%

1

2

4

12

9.00%

9.20%

9.31%

9.38%

9.00%

9.20%

9.31%

9.38%

m=

eff =

Quarterly

A person needs to borrow money. His neighborhood bank charges 11% interest

compounded semiannually. A downtown bank charges 10.8% interest

compounded monthly. At which bank will the person pay less interest?

(Hint: Compare the effective rates of each bank.)

(see the "Other Problem Types" tab)

Effective rate for neighborhood bank:

11.30%

OR

11.30%

Effective rate for downtown bank:

11.35%

OR

11.35%

Less interest is paid at the neighborhood bank.

Problem 14:

Bank #1 offers a money market account paying 4.5% interest compounded monthly.

Bank #2 offers a money market account paying 4.4% interest compounded daily.

(Assume 365 days in a year.) Which investment yields more money?

(see the "Other Problem Types" tab)

Bank #1 effective rate

4.59%

OR

4.59%

Bank #2 effective rate

4.50%

OR

4.50%

Problem 15:

A person invests $1600 in an account for 15 years. The annual interest rate is 7.5%

compounded quarterly for the first 9 years, then 9% compounded monthly for the

remaining years. At the end of 15 years, what is the value of this investment?

(see the "Other Compounding Periods" tab) - note that you'll find the amount after 9 years, and then take that as your present value for the last 6 years.

P=

$

i=

For last 6 years:

1.875% <--7.5% divided by 4.

n=

A after 9 years:

1,600.00

36 <--9 years; 4 quarters per year

$

3,122.87

P=

n=

A after 6 more years: $

(15 years total)

Problem 16:

In 5 years, a person will need a lump sum of $7500 to pay off a debt. How much

must be deposited today in an account that yields 6.25% interest compounded

monthly to amount to $7500 in 5 years?

(see the "Other Problem Types" tab)

A=

$

7,500.00

i=

0.52%

n=

60

P=

Problem 17:

$5,491.57

A $100,000 certificate of deposit held for 60 days was worth $101,133.33.

What is the present value of this investment? What is the future value of this

investment?

The $101,133.33 is the value after 60 days, so that is the future value.

The original value of $100,000 is considered the present value.

$

i=

3,122.87

0.750% <--9% divided by 12.

72 <--6 years; 12 months per year

5,348.09

Problem 18:

A company has agreed to pay $2.9 million in 6 years to settle as lawsuit. How

much must the company invest now in an account paying 8.4% compounded

quarterly to have this amount when it is due? (In other words, what is the

present value?)

(see the "Other Problem Types" tab)

A=

$

2,900,000.00

i=

2.10%

n=

24

P=

Problem 19:

$1,761,084.47

A accountant firm has ordered 7 new computers at a cost of $5,514 each. The

machines will be delivered in 7 months. What amount should the firm deposit

into an account paying 6.24% compounded monthly to have enough money to

pay for the computers when they arrive? (Find the present value.)

(see the "Other Problem Types" tab)

A=

$

38,598.00 Total cost of 7 computers

i=

0.52%

n=

7

P=

Problem 20:

$37,221.81

A developer needs $800,000 to buy land. He is able to borrow this amount at

11.5% per year, compounded semiannually. If he pays off this loan in 10 years, how

much of the payment will be interest?

(see the "Other Compounding Periods" tab) Note that A = P + I, so I = A - P.

P=

$

800,000.00

i=

5.75%

n=

20

A=

$

2,447,358.03

So a total of $2,447,358.03 will be paid back (A). $800,000 of this was the original principal amount borrowed, so the difference

$1,647,358.03 is the amount of interest charged.

Problem 21:

A consumer has a bill for $450. He has two choices: either pay the full amount

with no interest or pay $466.70 in two months with interest being compounded

monthly. If he chooses the second option, find the nominal (yearly) interest rate

that he would be charged.

(see the "Other Problem Types" tab - Example 4)

P=

450

A=

466.7

n=

2

i (periodic) =

1.84%

i (annual) =

22.06%

Problem 22:

A consumer has a bill for $1300. He has two choices: either pay the full amount

with no interest or pay $1385.92 in five months with interest being compounded

monthly. If he chooses the second option, find the nominal (yearly) interest rate

that he would be charged.

(see the "Other Problem Types" tab - Example 4)

P=

1300

A=

1385.92

n=

5

i (periodic) =

1.29%

i (annual) =

15.46%

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