Question

7. In order to purchase a house, you have taken out a 30 year mortgage of $200,000 at 4.29% interest per year. You make payments at the end of every month. What is the amount of each monthly payment?

Answer 1

This is the present value of annuity (P) calculation.

Given,

P = 200,000

Rate of interest = r = 0.0429

Number of years = n = 30

Number of months in a year = m = 12

Each monthly payment = A =?

Hence by the formula,

P = (A/(r/m)) [1 – {1 + (r/m)} ^ (-n × m)]

200,000 = (A/ (0.0429/12)) [1 – {1 + (0.0429/12)} ^ (-30 × 12)]

200,000 = (A/0.003575) [1 – {1 + 0.003575} ^ (-360)]

200,000 × 0.003575 = A [1 – (1/1.003575^360)]

715 = A [1 – (1/3.613601)]

715 = A [1 – 0.276732]

715 = A × 0.723268

715 / 0.723268 = A

A = 988.57 (Answer)