Question

HSBC decided to give Frank Broke a $500,000 mortgage loan at a rate of 4% for 30 years:

(a) What will be Frank’s monthly payments if he is expected to pay back the loan at the end of each month?

(b) How much interest and principal will Frank pay from the start of the second year (January) to the end of the third year (December)?

Answer 1

Answer a

We can use the present value of annuity formula to calculate the monthly loan payment

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Present value of annuity = mortgage loan amount = $500,000

P = monthly loan payment = ?

r = interest rate per month on loan = 4%/12 = 0.0033

n = number of monthly loan payments = 30 years x 12 = 360

500000 = P x {[1 - (1+0.0033)^-360]/0.0033}

500000 = P x 209.4612

P = 2387.08

Frank’s monthly payment = $2,387.08

Answer b

Amount of loan principal paid = Loan balance at the end of 1st Year - Loan balance at the end of 3rd Year

Calculation of loan balance at the end of 1st Year

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Present value of annuity = loan balance at the end of 1st Year = ?

P = monthly loan payment = 2387.08

r = interest rate per month on loan = 4%/12 = 0.0033

n = number of monthly loan payments remaining = 29 years x 12 = 348

Present value of annuity = 2387.08 x {[1 - (1+0.0033)^-348]/0.0033}

Present value of annuity = 2387.08 x 205.7726

Present value of annuity = 491194.82

Loan balance at the end of 1st Year = $4,91,194.82

Calculation of loan balance at the end of 3rd Year

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Present value of annuity = loan balance at the end of 3rd Year = ?

P = monthly loan payment = 2387.08

r = interest rate per month on loan = 4%/12 = 0.0033

n = number of monthly loan payments remaining = 27 years x 12 = 324

Present value of annuity = 2387.08 x {[1 - (1+0.0033)^-324]/0.0033}

Present value of annuity = 2387.08 x 197.9382

Present value of annuity = 472493.63

Loan balance at the end of 3rd Year = $4,72,493.63

Principal will Frank pay from the start of the second year (January) to the end of the third year (December) = $4,91,194.82 - $4,72,493.63 = $18,701.19

Principal will Frank pay from the start of the second year (January) to the end of the third year (December) = Loan outstanding at the start of 2nd year - Loan outstanding at the end of 3rd year

Interest will Frank pay from the start of the second year (January) to the end of the third year (December) = Total Loan payment with interest - Loan pricipal payment

Interest will Frank pay from the start of the second year (January) to the end of the third year (December) = [$2387.08 x 24 months] - $18,701.19

Interest will Frank pay from the start of the second year (January) to the end of the third year (December) = $57,289.84 - $18,701.19

Interest will Frank pay from the start of the second year (January) to the end of the third year (December) = $38,588.65