Question

Today, Malorie takes out a 20-year loan of $200,000, with a fixed interest rate of 4.9% per annum compounding monthly for the first 3 years. Afterwards, the loan will revert to the market interest rate.

Malorie will make monthly repayments over the next 20 years, the first of which is exactly one month from today. The bank calculates her current monthly repayments assuming the fixed interest rate of 4.9% will stay the same over the coming 20 years.

(c) Calculate the total interest Malorie pays over this fixed interest period.

Answer 1

To find the interest paid, we first need to find the monthly payment.

For that we can use the present value of annuity formula:

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

Substituting the values, we get:

Therefore, the monthly payment is $1,308.89

Now the total payment for first 3 years = $1,308.89 * (3*12) =  $47,119.97 .......(we will come to this amount later)

Now we need to find the principal balance at the end of this 3 year period or after the 36th (3*12) payment.

To find the balance of loan we can either make an amortization table or we can use a formula.

We will use the formula method to find this out here.

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

So the principal balance after 36th payment is $180,953.16

That means principal part paid till that date = $200,000 - $180,953.16 = $19,046.84

Total amount paid till that date is $47,119.97 ................(see note above)

Therefore, Total interest paid = Total amount paid - Principal part

= $47,119.97 - $19,046.84

=  28,073.13

Note: In the whole solution I have not rounded off intermediate calculations.