Question

A $200,000 mortgage was amortized over 25 years by monthly repayments. The interest rate on the mortgage was fixed at 4.30% compounded semi-annually for the entire period.

a. Calculate the size of the payments rounded up to the next $100.

Round up to the next 100

b. Using the payment from part a., calculate the size of the final payment.

Round to the nearest cent

Answer 1

Answer (a):

Effective annual Interest = (1 + 4.30%/2)^2 - 1 = 4.346225%

Monthly Interest = (1 + 4.346225%)^(1/12) - 1 = 0.35516480%

PV = $200,000

NPER = 25 * 12 = 300 MONTHS

Size of monthly payment = PMT(rate, nper, pv, fv, type) = PMT(0.35516480%, 300, -200000, 0, 0) = $1084.82

Size of monthly payment (Rounded up to the next 100) = $1100

Answer (b):

We calculated in answer a above, size of monthly payment = $1100

Let us first calculate NPER when PMT = 1100

Number of months = NPER (rate, pmt, pv, fv, type)

= NPER (0.35516480%, 1100, -200000, 0, 0)

= 292.7108775 Months

Balance at the end of month 292 = FV of Principal - FV of monthly installments

= 200000 * (1 + 0.35516480%) ^292 - 1100 * ((1 + 0.35516480%)^292 - 1) / 0.35516480%

= $779.5971

Size of the final payment = 779.5971 * (1 + 0.35516480%) = $782.37

Size of the final payment = $782.37