Question

You take a 12-years fixed rate loan at 5.0 % annual interest rate with initial principal of $400,000. The repayment is scheduled as quarterly instalments.

(a) Solve for your quarterly payment.
(6 marks)

(b) Three years later, you decide the change to monthly instalment for the remaining period at the same interest rate. Solve for the monthly payment. (12 marks)

(c) Calculate the total interest that you need to pay for the twelve years.
(2 marks)

Answer 1

a) Quarterly Payment:- This can be caluclated using the present value of annuity Present value of annuity is = P*(1-(1+r)^-n)/r Present value of annuity is = Loan = $ 400,000/. Pis Quarterly Payment = ? "r" is Quaterly interest rate is = 5.00%/4 = 1.25% "n" is No of quarters = 12*4 = 48 400000=P*(1-(1+0.0125)^-48)/0.0125 400000=P*0.449143511/0.0125) 400000=P*35.93148091 "P" is = (400000/35.93148091) "P" is = 5 11,132.30/. Approx. Your quarterly payment is = $ 11,132.30/. Amortization table for three years :- Beginning Interest Qtr balance Payment 400,000.00 5,000.00 393,867.70 4,923.35 387,658.75 4,845.73 381,372.18 4,767.15 375,007.03 4,687.59 368,562.32 4,607.03 362,037.05 4,525.46 355,430.21 4,442.88 348,740.79 4,359.26 341,967.75 4,274.60 11 335,110.05 4,188.88 328,166.62 4,102.08 Principle Payment 6,132.30 6,208.95 6,286.57 6,365.15 6,444.71 6,525.27 6,606.84 6,689.42 6,773.04 6,857.70 6,943.42 7,030.22 Total Payment 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 11,132.30 Ending balance 393,867.70 387,658.75 381,372.18 375,007.03 368,562.32 362,037.05 355,430.21 348,740.79 341,967.75 335,110.05 328,166.62 321,136.41 b) Beginning balance of fourth year is $ 321,136.41/. This is repaid in monthly installments for balance 9 years Now we need to compute the monthly repayment amount using above formula Present value of annuity is = P*(1-(1+r)^-n)/r Present value of annuity is = Loan = $ 321,136.41/. Pis Monthly Payment = ? "r" is Monthly interest rate is = 5.00%/12 = 0.4167% "n" is No of monthss = 9*12 = 108 321136.41=P*(1-(1+0.00416667)^-108/0.00416667 321136.41=P*0.361775677/0.00416667) 321136.41=P*86.82616257 "P" is = 5 3,698.61/. Approx. Your monthly payment is = $ 3,698.61. c) Total interest payment is = Total payments- 400000 Total interest payment is = ((11132.30*3*4)+(3698.61*9412))-400000) Total interest payment is = (533037.48-400000) Total interest payment is = $ 133,037.48/.