Question

(Solving for r of an annuity) You lend a friend $30,000, which your friend will repay in 5 equal annual end-of-year payments of $8,000, with the first payment to be received 1 year from now. What rate does your loan reciece?

The rate of return your loan will receive is ____%(round to two decimal places)

Answer 1

Amount lent = $30,000

Annual payments = $8,000 (made at the end of each year)

Number of years = 5

Interest rate is calculated as below:

$30,000 = $8,000/(1+r)^1 + $8,000/(1+r)^2 + $8,000/(1+r)^3 + $8,000/(1+r)^4 + $8,000/(1+r)^5

Solving for r, by trial and error,

• for r = 20%, Present value = $35,981.22
• for r = 25%, present value = $ 31,344.64
• For r = 26.667%, present value of the annual payments equal to $30,000.

Hence, the interest rate on the loan is 26.67%