Question

Today, Malorie takes out a 10-year loan of $200,000, with a fixed interest rate of 5.7% 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 10 years, the first of which is exactly one month from today. The bank calculates her current monthly repayments assuming the fixed interest rate of 5.7% will stay the same over the coming 10 years.

(a) Calculate the size of the repayment that the bank requires Malorie to make at the end of the first month.

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

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

(d) After the fixed interest period, the market interest rate becomes 6.7% per annum effective. Assuming the interest rate stays at this new level for the remainder of the term of the loan, calculate the new monthly installment.

Answer 1

a.
Formula to calculate monthly payment
Monthly payment	Present value/(1-((1+r)^-n)/r)
No of payments (n)	120	10*12
Monthly interest rate (r)	0.48%	5.7%/12
Monthly payment	200,000/(1-(1.0048^-120)/0.0048))
Monthly payment	200,000/91.30755
Monthly payment	$2,190.40
b.
Calculate value of loan after three years
Value of loan	Monthly payment*(1-(1+r^-n)/r)
Value of loan	2190.40*(1-(.0048^-120)/0.0048)
Value of loan	2190.40*69.13161
Value of loan	$151,425.83
Total interest paid	(2190.40*36)-(200000-151425.83)
Total interest paid	$30,280.21
d.
Calculation of revised monthly payment
No of payments (n)	84	7*12
Monthly interest rate (r)	0.56%	6.7%/12
Monthly payment	151425.83/(1-(1.0056^-84)/0.0056))
Monthly payment	151425.83/66.90551
Monthly payment	$2,263.28
Thus, the new monthly instalment would be $2,263.28