Answer to Question #162223 in Financial Math for suzy

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

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