Answer to Question #164454 in Financial Math for PAJANA

Question

Rania buys an apartment for RM 315,000 with 15 % down payment. She takes a loan from a bank to settle the balance at an interest rate of 4.2 % compounded monthly. She is required to pay equal monthly payments for 25 years to settle the loan. (a) Calculate the monthly payment. {3 marks} (b) Calculate the total interest charged. {2 marks} (c) If Rania fails to make the first four monthly instalments, how much could she pay on the fifth month to settle all the outstanding arrears? {2.5 marks} (d) After paying for 20 years, Rania decides to settle the loan in full. Calculate the full settlement for Rania. {2.5 marks}

Answer 1

$315 000 -0.15\times315000=267 750$ - balance

a) monthly payment find the formula:

$A=S\times\frac{r(1+r)^n}{(1+r)^n-1}$

S=267 750

$r=\frac{0.042}{12}=0.0035$

$n=25\times12=300$

put in the above formula:

$A=S\times\frac{r(1+r)^n}{(1+r)^n-1}=267 750\times\frac{0.0035(1+0.0035)^{300}}{(1+0.0035)^{300}-1}=1443.02$

b) $1443.02\times300-267750=165156$

c)$1443.02\times5=7215.10$

d) find the formula:

Calculate rebate based on the ‘Rule of 78’

$\frac{(n-3) (n-2) \times I}{ N(N+1)} = R$

R= Rebate (RM)

n= Number of Monthly Installments over the unexpired period

N= Loan Tenure

I= Interest payable for the whole Loan Tenure (RM)

N=300

$20\times12=240$

n=300-240=60

$I =267750\times\frac{4.2}{100}\times25 =281137.5$

put in the above formula:

$\frac{(60-3)(60-2) \times 281137.5}{ 300(300+1)} = 10292.81$

$1443.02*(300-240)-10292.81=76288.39$ - the balance of the payment with a discount

$1443.02*300-10292.81=422613.19$ - the entire payment amount loans with interest after 20 years at a discount