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.

(b) Calculate the loan outstanding at the end of the fixed interest period (i.e. after 3 years).

Answer 1

Frequency of conversion,m = 20*12 = 240

Rate, r = 4.9/12%

Present Value = 200,000

Present Value Factor = (1 - (1+r)^-m)/r = (1-(1+4.9/12%)^-240)/r = 152.80

Amount of Repayments per month(A) = 200,000/Present Value Factor = 200,000/152.80 = 1,308.89$

Hence, the repayment amount including interest and principal comes out to be 1,308.89$

Loan outstanding at the end of the fixed interest period or at the beginning of the 4th year  

We need to find the amount left after the end of 3 years. So that will be given by 240-36+1 = 205 months. We have taken 36 months cause we have charged interest for 24 months in this period and added to find the amount at the end month of 3rd year or beginning of the 4th year.

This is given by A(1-(1+(4.9/12%)^-205)/4.9/12%

So loan outstanding after the end of the fixed interest rate period = A(1-(1+(4.9/12%)^-205)/4.9/12%

= 181,255.01 (You can find all the values from the internet or use excel to calculation)

Hence the amount outstanding at the end of the 3rd year is $181,255.01