Question

Today, Malorie takes out a 30-year loan of $200,000, with a fixed interest rate of 4.5% 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 30 years, the first of which is exactly one month from today. The bank calculates her current monthly repayments assuming the fixed interest rate of 4.5% will stay the same over the coming 30 years.

(d) After the fixed interest period, the market interest rate becomes 5.5% 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

Interest rate per month = 4.5%/12 = 0.375% = 0.00375

No. of months = 30*12 = 360

Monhly Installment for 30 year loan ( A ) is given by equating present value of installments to the loan amount

=> A/0.00375*(1-1/1.00375^360) = 200000

=> 197.361159 *A = 200000

=> A =$1013.37

Amount of loan outstanding after 3 years (36 months)

= Future value of loan - Future value of 36 payments

=200000* (1+0.00375)^36 - 1013.37/0.00375*(1.00375^36 -1)

= $189869.19

The new Installment amount (P) for the remaining loan for 27 years = 324 months at an effective rate of 5.5% is given by

P/1.055^(1/12)+ P/1.055^(2/12) + ... +P/1.055^(324/12) = 189869.19

Applying the sum of GP formula

=> P/1.055^(1/12) * (1- (1/1.055^(1/12))^324) / (1-1/1.055^(1/12)) = 189869.19

=> 170.940734* P = 189869.19

=> P = $1110.73

So, the new monthly installment will be $1110.73

Alternatively , Effective annual rate of 5.5% implies a per month rate = 1.055^(1/12) -1 =0.004472

So, the new Installment amount (P) is given by

P/0.004472*(1-1/1.004472^324) = 189869.19

=> 170.940734* P = 189869.19

=> P = $1110.73

So, the new monthly installment will be $1110.73