Question

Jennifer is saving up for the closing costs ($4250) and down payment on a home. For a better interest rate and savings on mortgage insurance, she must have a down payment of 10%. She can afford a monthly payment of $900 based on her current earnings and expenses. The amount available for the mortgage is reduced by an estimated $175 per month to cover home insurance and real estate taxes. The current nominal annual interest rate is 3% for a 30-year fixed-rate mortgage loan. How much of a loan can she afford

Answer 1

The amount of Loan Jennifer can afford is $171,962.30.

Step-by-step explanation:

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or the amount of Loan Jennifer can afford =?

P = Monthly payment for the mortgage = Monthly amount she can afford - Estimated monthly home insurance and real estate taxes = $900 - $175 = $725

r = Monthly nominal interest rate = Annual nominal interest / 12 = 3% / 12 = 0.03 / 12 = 0.0025

n = number of months = Number of years * 12 = 30 * 12 = 360

Substitute the values into equation (1) to have:

PV = $725 * ((1 - (1 / (1 + 0.0025))^360) / 0.0025)

PV = $725 * 237.189381504283

PV = $171,962.30

Therefore, the amount of Loan Jennifer can afford is $171,962.30.