Answer to Question #163695 in Financial Math for Dayalan

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.

(b) Calculate the total interest charged.

(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?

(d) After paying for 20 years, Rania decides to settle the loan in full. Calculate the full settlement for Rania.

Answer 1

(a)

Down payment will be$=15/100*315000=47250$

Balance will then be

$=315000-47250=267750$

Monthly payment

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

S=267 750

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

$n=25\times12=300$

$Q=267750×0.0035(1+0.0035)300/(1+0.0035)300​-1=1443.02$ $​$

(b)

$=1443.02×300−267750=165156$

(c)

$=1443.02×5=7215.10$

(d)

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:

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

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

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