Question

QUESTION 2: LOAN AMORTIZATION [35 MARKS]

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)

Answer 1

A. Value of the mortgage on the house

Price of the house = $326,000

Deposit Amount = $75,000

Mortgage value (MV) = House Price – Deposit Amount

MV = $326,000 - $75,000 = $ 251,000

B. Value of the monthly payment

T= 30 years

Tmonths = $30\times 12 = 360 months$

J₁₂ = 9%

Interest rate per month = $9 \times 12 = 0.75$ % per month

Monthly payments (PMT) = $251,000 \times 0.75 \times 1.0075^{360} / ( 1.0075^{360} -1)$

PMT = $ 2019.6

C. Loan outstanding after making 20 payments

Outstanding balance T_months = 360 – 20 = 340 months

Monthly payments (PMT) = $2019.6

Loan outstanding = $2019.6 \times (1- 1.0075^{-340} )/ (0.0075)$

Loan outstanding = $2019.6 \times 0.92117 / 0.0075$

Loan outstanding = $ 248,053.2

D. Principal repaid in the 21st payment

Principal = P₃₄₀-P₃₃₉

P₃₃₉ = $2019.6 \times (1- 1.0075^{-339}) / 0.0075$

P₃₃₉ = $ 247,893.95

The principal paid in the 21^st payment = $248,053.15 - $247,893.95

P₂₁ = $ 159.20