Question

Hadley’s tuition for the coming school year is due today. He borrows $10,000 from his uncle and agree to repay $12,500, three years from today. What is the interest rate of this loan?

1. 5.51%
2. 6.67%
3. 7.72%
4. 8.06%
5. 7.46%

Answer 1

Formula for compound interest can be used to compute interest rate as:

A = P x (1 + r/n) ^nt

A = Total loan repayment including interest = $ 12,500

P = Principal of loan = $ 10,000

r = Rate of interest

n = No. of compounding in a year = 1 [Assumed as it is not mentioned]

t = No. of years = 3

Substituting all the values and solving, we get r as:

$ 12,500 = $ 10,000 x (1+r) ^1x3

                = $ 10,000 x (1+r) ³

(1+r) ³ = $ 12,500/$ 10,000

              = 1.25

1+r = (1.25)^1/3

1+r = (1.25)^0.333333

1+r = 1.077217345

r = 1.077217345 - 1

r = 0.077217345 or 7.72 %

Hence option “3. 7.72%” is correct answer.