Question

a debt of 500 dollars is paid 25 dollars every end of the year for 30 years, if the borrower replaces the debt principal with a sinking fund that produces an effective annual interest rate of 1.5%, calculate the annual effective interest rate paid by the borrower on this debt. Choose the answer that is closest!

a) 1,54%
b) 2,43%
c) 2,90%
d) 3,54%
e) 3,90%

dont use excel!! manually!!

Answer 1

The correct answer is option d) 3,54%

We need not use excel, but we will have to use the financial calculator.

Straight Debt:

A debt of 500 dollars is paid 25 dollars every end of the year for 30 years,

If i is the interest rate then, use the financial calculator to calculate the interest rate.

i = ? when n = 30, PMT = 25, PV = -500, FV = 0

i = 2.8%

Sinking fund:

A sinking fund that produces an effective annual interest rate of j = 1.5% is good enough to take care of loan principal of $ 500 after 30 years.

Let's assume the contribution towards sinking fund per annum be S. Hence FV of S over 30 years should be good enough to take care of the loan of $ 500

Hence, S / j x [(1 + i)^N - 1] = S / 1.5% x [ (1 + 1.5%)³⁰ - 1] = 37.54S = 500. hence, S = 500 / 37.54 = 13.32

Annual interest portion = i x $ 500 = 2.8% x $ 500 = $ 14

Hence total annual payment per annum = interest portion + contribution towards sinking fund = 14 + 13.32 = 27.32

If i' is the annual effective interest rate paid by the borrower on this debt, then PV of all future payment at R should be the loan amount today.

Hence we have to find R. Use financial calculator:

i' = ?, n = 30, PMT = 27.32, PV = -500, FV = 0

i' = 3.54%

Hence, the correct answer is option d) 3,54%