Answer to Question #121668 in Financial Math for Lileean

Question

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)
E. 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?

Answer 1

A. Value of the mortgage on their house

Mortgage value = $326,000

Deposit = $75,000

Mortgage Value = Amount – Deposit

Mortgage Value = $326,000 - $75,000 = $ 251,000

B. Value of the monthly payment?

T= 30 years

Tmonths = 30*12 = 360 months

J₁₂ = 9%

Interest rate per month = 9% / 12 = 0.75% per month

PMT = 251,000 (0.75%) * (1.0075)³⁶⁰ / ( (1.0075)³⁶⁰ -1)

PMT = $ 2019.6

C.Loan outstanding after making 20 payments

Balance T_months = 360 – 20 = 340 months

PMT = $2019.6

Amount = 2019.6 * 1- (1.0075)^-340 / (0.0075)

Amount = 2019.6 * (1- (1.0075)^-340) / (0.0075)

Amount = $ 248,053.2

D. Principal repaid in the 21st payment

Principal = P₃₄₀-P₃₃₉

P₃₃₉ = 2019.6 * (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

E. Loan amortization schedule.

The beginning balance is the mortgage value which is equal to $251,000. The interest is computed by multiplying the interest rate (0.75% per month) by beginning balance (Beginning balance * Interest rate per month). The principal is obtained by dividing the monthly payment of 2019.6 by the discount factor computed as (1.0075)ⁿ The ending balance is computed by getting the different between the beginning balance and the principal amount (Ending Balance = Beginning balance – Principal).The loan amortization schedule for the first 5 payments is given as follows:

Composition of the payment amount.

From the schedule, it can be noted that the interest decreases and principal increases at a uniform rate/amount of $1.03 and $1.05 over the 5 year period. The marginal interest and principal incremental is spread out across the years until the mortgage upto the last payment.