Question

QUESTION 3 You took a loan in the amount of RM29,746.39. You were told that you have to make end-of- year annual repayments as per the schedule below. Year D Annual Repayment RM? RM? RM? RM1,500 RM2,000 RM3,500 RM5,000 RM7,500 RM7,500 RM12,000 If the annual rate of interest is 4.5% (annual compounding), calculate the missing cash flows (annual repayment for years 1, 2 and 3). The annual repayment for years 1, 2 and 3 is the same amount. (7 marks)

Answer 1

Present value of all future annual repayments at given interest rate is equals to the initial value of Loan amount. This can be expressed with following equation:

$\small \textup{Loan Amount} = \frac{AP_1}{(1+i)^1}+\frac{AP_2}{(1+i)^2}.........+\frac{AP_n}{(1+i)^n}$

where,

AP = Annual repayment

i = interest rate

Lets assume Annual payments for first 3 years is X.

$\inline \dpi{200} \tiny 29,746.39 = \frac{X}{(1+0.045)^1}+\frac{X}{(1+0.045)^2}+\frac{X}{(1+0.045)^3}+\frac{1,500}{(1+0.045)^4}+\frac{2,000}{(1+0.045)^5}+\frac{3,500}{(1+0.045)^6}+\frac{5,000}{(1+0.045)^7}+\frac{7,500}{(1+0.045)^8}+\frac{7,500}{(1+0.045)^9}+\frac{12,000}{(1+0.045)^{10}}$

$\inline \dpi{200} \tiny 29,746.39 = X\left (\frac{1}{(1+0.045)^1}+\frac{1}{(1+0.045)^2}+\frac{1}{(1+0.045)^3} \right )+\frac{1,500}{(1+0.045)^4}+\frac{2,000}{(1+0.045)^5}+\frac{3,500}{(1+0.045)^6}+\frac{5,000}{(1+0.045)^7}+\frac{7,500}{(1+0.045)^8}+\frac{7,500}{(1+0.045)^9}+\frac{12,000}{(1+0.045)^{10}}$  

$\inline \dpi{150} \small 29,746.39 = X*(0.9569+0.9157+0.8763)+1,257.84+1,604.90+2,687.64+3,674.14+5,273.89+5,046.78+7,727.13$

$\inline \dpi{150} \small 29,746.39 = X*(2.7490)+27,272.32$

$\inline \dpi{150} \small X*(2.7490) =29,746.39-27,272.32$

$\inline \dpi{150} \small X*(2.7490) =2,474.07$

$\inline \dpi{150} \small X =\frac{2,474.07}{2.7490}$

$\inline \dpi{150} \small X = 899.98$

$\inline \bg_green \LARGE X = 900$

Thus, Annual repayment for first 3 years is RM900

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.