Question

Kirk has a 4.5 year loan of $50,000 with St George Bank. He plans to repay the loan in 9 equal semi-annual instalments starting today. If the rate of interest is 8.4% p.a. compounding semi-annually, how much will each repayment be worth?

Select one:

a. $6,481.73

b. $6,352.98

c. $6,280.74

d. $6,104.08

Answer 1

This can be solved using present value of annuity immediate formula

Present value of annuity immediate = P+[P*(1-(1+r)^-(n-1))/r]

"P" is Semi annual payment = ?

"r" is Semi annual interest rate = 8.40%/2 = 4.20%

"n" is No of Semi annuals = 9

Present value of annuity immediate = Loan = $ 50,000/.

50000=P+[P*(1-(1+0.0420)^-(9-1))/0.042]

50000=P+[P*6.677488615]

50000=7.677488615*P

P is = (50000/7.677488615)

P is = $ 6,512.55/. Approx.

Semi annual payment is $ 6,512.55/.

Nearest answer is Option a)