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

PV of loan =200000
Rate per month =5.7%/12
Number of months =10*12 =120

a. Size of monthly payment =PV/((1-(1+r)^-n)/r =200000/((1-(1+5.7%/12)^-120)/(5.7%/12)) =2190.3993

b. Balance after 36 months =PV*(1+r)^n-PMT*((1+r)^n-1)/r =200000*(1+5.7%/12)^36-2190.3993*((1+5.7%/12)^36-1)/(5.7%/12))=151425.8320

c. Interest payment over the period =Number of monthly Payments*36-(PV of loan -Balance after 36 months )
=2190.3993*36-(200000-151425.8320) =30280.21

d. Rate per month =6.7%/12
Number of Periods left =12*7 =84
Balance after 36 months =151425.8320
Size of monthly payment =PV/((1-(1+r)^-n)/r =151425.8320/((1-(1+6.7%/12)^-84)/(6.7%/12)) =2263.28