Question

A 10-year loan of 2000 is to be repaid with payments at the end of each year. It can be repaid under the following two options:

(i) Equal annual payments at an annual effective interest rate of 5%.

(ii) Installments of 200 each year plus interest on the unpaid balance at an annual effective interest rate of i.

The sum of the payments under option (i) equals the sum of the payments under option (ii).

Calculate i.

Answer 1

For method (i), using

N= 10,

i = 5

P.V = 2000,

F V= 0 and END, we get

X_a10= 2000

X = 2000 / 7.7217

X = 259

So the total payment for the 10 years is 2590

ii) Under option ii, there is a flat payment of 200 per year plus a decreasing payment of

i[2000 + 1800+ 1600…+200]

= 200 i [10+9+..1]

= 200 i [55] = 11,000 i.

Principal payments are (10)(200).

Total payments = 2000 + 11,000 i = 2,590.

Hence i = 0.0536 or 5.36 %