Question

Your tuition for the coming year is due today. You borrow $8,000 from your uncle and agree to repay in the three years an amount of $9,250. What is the interest rate on this loan

Answer 1

Interest rate on the loan is approximately 5%

Step-by-step explanation:

The interest rate on the loan can be found by using the compound interest formula.

FV = P(1 + r)^t

Where: FV = Future value

P = Principal amount

r = Interest rate

t = Time period in years.

FV = $9,250

P = $8,000

t = 3 years

r = unknown

Substitute the values above into the formula

9,250 = 8,000 (1+r)^3

Divide both sides by 8000

9,250/8000 = (8,000 (1+r)^3)/8000

1.15625 = (1+r)^3

Find the cube root of both sides

`\sqrt[3]{ 1.15625}` =
`\sqrt[3]{(1+r)^3}`

1.049584113 = 1+r

Subtract 1 from both sides

1.049584113 - 1 = 1+r - 1

0.049584113 = r

r = 0.049584113

r ≈ 0.05 = 5%

That is, the interest rate on the loan is approximately 5%