Simple interest

When someone pays or receives simple interest (I), he or she pays or receives interest on the principal only, not on the interest that has already been paid. To find the interest you can use the following formula.

Simple interest formula

What types of loans use simple interest?

A few exercises showing how to compute or find the simple interest

Exercise #1:

Compute the interest if the principal amount is 2000 dollars at a rate of interest of 5% for 4 years.

I = p × r × t

p = 2000, r = 5%, and t = 4

Interest = 2000 × 5% × 4

Interest = 2000 × 0.05 × 4

Interest = 100 × 4 = 400

After 4 years, the simple interest on a 2000 principal is 400 dollars.

Exercise # 2

Suppose you inherited a lump sum of 2 millions dollars. Compute the interest if the principal amount is 2,000,000 dollars at a rate of interest of 4% for a year.

I = p × r × t

p = 2000,000, r = 4%, and t = 1

Interest = 2,000,000 × 4% × 1

Interest = 2,000,000 × 0.04 × 1

Interest = 80,000 × 1 = 80,000

If you have 2 millions dollars and your bank pays you 4% interest every year, you will earn 80,000 dollars every year.

Great, you can perhaps quit your day time job!

Exercise # 3

Compute the interest if the principal is 100 dollars at a rate of interest of 2% for 10 years.

I = p × r × t

p = 100, r = 2%, and t = 10

Interest = 100 × 2% × 10

Interest = 100 × 0.02 × 10

Interest = 2 × 10 = 20

How to find the principal when the end balance is known

End balance  = money invested  + simple interest 

Let P be the money invested

End balance  = P + Prt

End balance  = P(1 + rt)

Exercise # 4

The end balance of an auto loan after 5 years is 38150. Find the price of the car if the annual interest is 1.8 %.

Use r = 1.8% = 1.8/100 = 0.018

Use t  = 5

End balance  = P + Prt

38150 = P(1 + 0.018 × 5)

38150 = P(1 + 0.09)

38150 = P(1.09)

38150 / 1.09 = P 

P = 35000

The price of the car is $35000.

How to find the annual interest rate

Exercise # 5

Find the annual percentage rate (APR) if the amount of money you invested in a company has doubled after 8 years.

Let P be the initial principal or the amount that you invested.

Then, the end balance is 2P.

End balance  = P(1 + rt)

2P  = P(1 + 8r)

2 = 1 + 8r

2 - 1 = 8r

1 = 8r

1/8 = r

r = 0.125

r = 12.5%

The APR is 12.5%

How to find the time when the total interest is known

Exercise # 6

How long does it take to get a total interest of $5760 if the principal is $16000 and the interest rate is 3%.

Interest = Principal × Interest rate × Time 

5760 = 16000 × 3% × Time

5760 = 16000 × 0.03 × Time

5760 = 480 × Time

Time = 5760 / 480

Time  = 12 years

Take the simple interest quiz to see if you really understood this lesson

Some questions are tricky. Read carefully before answering a question!