Question

You take out a home loan of $500 000, which will be repaid in 40 level payments at the end of each six-month period, starting in six months. The annual interest rate is 5%.

(a) Compute the size of the repayments if interest is compounded every six months.

(b) Suppose instead that interest is compounded monthly but repayments are still made every six months. Determine the equivalent annual interest rate for payments made every six months and find the size of the repayments. To compute the repayments, round the equivalent annual interest rate to three significant figures.

Answer 1

Answer:

a) Formula to compute compound interest is given as follows:

  

nt

Here P = Amount Loaned, r = annual interest rate, and n = no of compound periods , t is time

Interest is compounded every six months, so,

P = 500,000 , r = 5%, t = 40 levels = 20 years, n = 6

  

24-20 500000(1.025)40 1342532 C 500000(1 2

Size of repayment = 1342532/40 = 33563.29

b) For monthly,

C 500000(1 1220500000 1.0041)240 1356320

size of repayment = 1356320/40 = 33908

and the equivalent annual interest is given by,

  

q x |(1 1 El

Here m = 12, q = 2 and r = 5

Putting all these vales in above equation we get

i = 5.0524