Question

A homebuyer wishes to finance the purchase with a $95,000 mortgage with a 20-year term. What is the maximum interest rate the buyer can afford if the monthly payment is not to exceed $900?

Answer 1

Answer:

0.811% per month is the amximum rate it can affor

or 9.732% annual rate with monhly compounding.

Explanation:

We have to solve for the rate at which the monthly payment equals 900 dollars.

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 900.00

time 240

rate r

PV $95,000.0000

$900 \times \frac{1-(1+r)^{-240} }{r} = 95,000$

Given the complexity of the formula we solve using excel or a financial calcualtor

we write on a1 =PV(A2;240;95000)

on a2 we write any number between 0 and 1

then we use goal seek tool adn define that we want A1 to be 95,000 by changing A2 (which is the argument for rate)

the value of A2 after this is our answer:

$900 \times \frac{1-(1+0.00811)^{-240} }{0.00811} = PV$

PV $95,000.0000