How to set up and answer interest problems

Question

The Thorntons have just welcomed their second child into their family. Due to the increased size of their
family, they decide to move out of their little 2 bedroom apartment. They have saved $20,000 over the last
few years in anticipation of this move. They plan to use this money toward a down payment on a house. Local
mortgage rates are 4.5% per year compounded monthly for a conventional 30-year mortgage and they estimate
they can afford to pay at most $800 a month on the mortgage.

 

Determine the list price of the most expensive house they should consider purchasing.

If they purchase the most expensive house they can afford, how much interest will they pay over the
course of the loan (assuming they make the scheduled payments and no more or less)?

Answer 1

c = (Pr(1 + r)ⁿ) / ((1 + r)ⁿ - 1), where c = monthly payment, P = principal, r = monthly rate, n = number of payments.

c = 800

r = 0.045/12 = 0.003750

n = 360

 

800 = (P(0.045)(1.00375)³⁶⁰ ) / ((1.00375)³⁶⁰ - 1 )

800 = (P(0.045)(3.8476980)) / (3.8476980 - 1)

800 = 0.01731P / 2.8476980

2278.16 ≈ 0.01731P

131609.38 = P

 

They could afford a home listed at 131,609.38 + 20,000 or $151,609.38.