Question

I. A family buys a house worth $326,000. They pay $75,000 deposit and take a mortgage for the balance at J12=9% p.a. to be amortized over 30 years with monthly payments.

A. Find the value of the mortgage on their house? (1 mark)
B. Find the value of the monthly payment? (3 marks)
C. Find the loan outstanding after making 20 payments? (4 marks)
D. Find the principal repaid in the 21st payment? (5 marks)

II. Fill out the loan amortization schedule provided in the solution template for the first 5 loan payments. What do you notice about the composition of the payment amount? (6 marks)

Answer 1

A)  $S=(326,000−75,000)=251,000$

S-sum of mortgage

B) $P=251,000∗ \frac{0.09/12∗(1+0.09/12)^{360}}{(1+0.09/12) ^{360}−1}=2019.6$

P-payment

C) the loan outstanding after making 20 payments is:

$S20= 2019.6*\frac{1-1.0075^{340}}{1-1.0075}/1.0075^{340}$

$S20=248,053.15$

S20-sum of mortgage after 20 payments

D) $248,053.15*1.0075=249,913.55$

II) The loan amortization schedule for the first 5 loan payments.

$S_1=S*i-P$

$S_2=S_1*i-P$

Sn -certain year sum

i-interest rate=1.09/12=1.0075

P-payment=2019.6

payment balance

1) 2019.6 250,862.9

2) 2019.6 250,724.77

3) 2019.6 250,585.61

4) 2019.6 250,445.4

5) 2019.6 250,304.14

I noticed the share of interest payments becomes less.