Math >> Money and Finance

# Money Math

## Interest and Percent

Below are money word problems that calculate interest and percent. The student will also need to understand the units of United States currency including coins (dimes, nickels, etc.), cents, and dollars. You might need a special calculator for some of the calculations, but a lot of phones have the "x to the power of y" feature needed for compound interest.

Formulas Needed

There are two main formulas you will need for the problems on this page:

Simple interest

I = P x r x t

where I = Interest, P = principal, r = interest rate, t = time

Compound interest

Future Value = P x (1 +rn)nt

where P = principal, r = interest rate, t = time in years, n = number of times per year interest is compounded

Compound Interest = Future Value - P

Practice Problems

1) You invested \$1272 in a business. At the end of the year, you earn 3% interest. How much money did you earn?

This is simple interest as it wasn't being compounded throughout the year. So you use the simple interest formula:

I = P x r x t

P = the principal or \$1272 in this case

r = interest rate which is 3%. We write that as 3/100 or .03 in the formula.

t = time, in this case that is 1 for 1 year

I = 1272 x .03 x 1

I = \$38.16

2) You put \$3000 in the bank. The money earns a simple interest rate of 2.5%. How much money will you earn in interest over the next 10 years?

I = P x r x t

I = \$3000 x .025 x 10

I = \$750

You will earn \$750 in interest over 10 years.

3) Consider problem number 2 now with compounding interest. You put \$3000 in the bank at an interest rate of 2.5%. Now the interest is compounded monthly. How much interest will you earn over 10 years? How much more interest did the deposit earn with compound interest vs. simple interest?

Future Value = P x (1 +rn)nt

P = principal which is \$3000

r = interest rate which is 2.5% or .025

t = time in years which is 10

n = number of times per year the interest is calculated which is 12 for each month of the year

FV = 3000 x (1 +.02512)10 x 12

FV = 3000 x 1.28369154...

FV = \$3,851.07

Now subtract the original principal from the future value to get the compound interest:

Compound interest = \$3,851.07 - \$3,000 = \$851.07

For the second part of the problem we compare the compound interest with the simple interest figured in problem #2:

Compound interest - Simple interest

\$851.10 - \$750 = \$151.10

You can see that by using compound interest the deposit earned an additional \$151.10.

4) If you invested \$5000 in a fund that earned 5% interest compounded quarterly, what would be the final value of the investment after seven years?

In this case we can just use the future value formula for compound interest:

Future Value = P x (1 +rn)nt

P = \$5000

r = 5% or .05

t = 7 (for seven years)

n = 4 (this is because quarterly is every 3 months or four times per year)

FV = 5000 x (1 +.054)7 x 4

FV = \$7,079.96

The investment will be worth \$7,079.96 after seven years.