Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $96. If the interest that was collected was simple interest, what was the annual interest rate?

Question

Mathematics

Alayna Gray

17 November, 02:50

Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $96. If the interest that was collected was simple interest, what was the annual interest rate?

+2

Answers (1)

Know the Answer?

Breanna Hoffman · Answer 1

The annual interest rate was 4%

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Loan to Kenneth's niece to buy a computer = US$ 1,200

Duration of the loan = 2 years

Niece paid back to Kenneth = US$ 1,296

Annual interest rate = x%

2. Let's find the annual interest rate after 2 years, using the following formula:

FV = PV * (1 + x)

PV = Loan to Kenneth's niece to buy a computer = US$ 1,200

FV = Niece paid back to Kenneth = US$ 1,296

rate (r) = x

Replacing with the real values:

1,296 = 1,200 * (1 + x)

1.296/1.200 = (1 + x) (Dividing by 1,200 at both sides)

1.08 = 1 + x

1.08 - 1 = x (Subtracting 1 at both sides)

0.08 = x

This is the interest rate for two years, for finding the annual interest rate we divide it by 2, this way:

0.08 / 2 = 0.04 * 100 = 4%