Question

You have just taken out a 30‑year mortgage on your new home for $103,104. This mortgage is to be repaid in 360 equal monthly installments. If the stated (nominal) annual interest rate is 13.35 percent, what is the amount of each of the monthly installments? (Note: The convention when periodic payments are involved is to assume that the compounding frequency is the same as the payment frequency, unless stated otherwise. Thus this implies 13.35 % APR, compounded monthly for this problem. To compute the correct payment, do not round your interest rate too much.)

Answer 1

Answer; Part (A)

Current Monthly Installment Amount =

No of Year = 30 Years

No of period = 30 X 12 = 360 monthly payments

Rate = 13.35% per annum

Monthly rate = 13.35 % / 12 = 1.1125%

Principal Amount = $ 103,104

Formula ; Monthly Installment = = P × r × (1 + r)n/((1 + r)^n - 1)

= 103,104 x 1.1125% [ (1.011125)^360/ (1.011125)^300 -1]

= 1147.032 x[53.67171006/(53.67171006-1)]

= 1147.032 X 1.018985524

= $1168.81 Per Month or $1169