Question

A $40,000 mortgage loan charges interest at 6.6% compounded monthly for a four-year term. Monthly payments were calculated for a 15-year amortization and then rounded up to the next higher $10.

a) What will be the principal balance at the end of the first term?

b) What will the monthly payments be on renewal for a three-year term if it is calculated for an interest rate of 7.2% compounded monthly and an 11-year amortization period, but again rounded to the next higher $10?

Answer 1

First let us find the monthly payment. For that we can use the Present value of annuity formula:

Where,
PVA = Present Value of Annuity
A = Annuity / Payment
i = rate of interest
n = number of years
a = number of payments per year
na = number of payments

Since the problem asks us to round off the payment to next $10, it will be $360 Per month.

a) Now let us find the Principal balance after the four year term, that is balance after 48th payment.

For that we can use the following formula:

Where,
PV = Present value / original balance
A = Annuity / Payment
i = rate of interest
a = number of payments per year
n = number of years
na = total number of payments

Therefore, the principal balance at the end of the first term is $32,333.43

b)

We can use the same formula for present value of annuity to find the monthly payment.

Rounding it off to the next higher $10 will become $360 per month.