Question

Rino just purchased his first car with a 7.5% 5 year mortgage loan of RM78,000. (a) If he pays interest yearly and the total loan will be settled at the end of year 5, how much is his equal yearly payment for the sinking fund which earns 5.2% interest yearly compounding? Assume that the first payment to the fund make immediately. (b) Refer to part (a), if Rino did not pay interest to the lender for the whole tenure till end of year 5 and the first payment make to the sinking fund is one year from now, find the equal yearly payment to the fund.

Ans: (a) RM 13,364.78 (b) RM 20,184.59

(Pls dun answer in excel format, pls attch the formula used)

Answer 1

a. Future Value Interest Factor of Immediate Annuity of RM 1 at 5.2 % for 5 years = [ { ( 1 + r ) ⁿ - 1 } / r ] x ( 1 + r ) = [ { ( 1.052) ⁵ - 1 } / 0.052 ] x 1.052 = 5.83623 ( Note: You use future value interest factor in a sinking fund problem )

Yearly payment = $ 78,000 / 5.83623 = $ 13,364.79

b. The amount of the loan to be repaid = $ 78,000 x ( 1.075 ) ⁵ = $ 111,979.09

Future Value Interest Factor of Ordinary Annuity of RM 1 at 5.2 % for 5 years = [ { ( 1.052) ⁵ - 1 } / 0.052 ] = 5.54775

Equal yearly payment required = $ 111,979.09 / 5.54775 = $ 20,184.59