Question

You are shopping for a house and wonder what you can afford. Banks look at collateral, creditworthiness and capacity (ability to pay) when making loans. Assume you have sufficient downpayment and credit score. Your bank has a requirement of 28% housing expense ratio and your gross monthly income is $5,450. How much can you afford to pay in principal, interest, taxes an insurance (PITI) each month?

Show how you calculated how much you can afford to spend on a home in the previous question.

You are looking to purchase a new home that is listed at $315,100. You have saved enough to make a 20% downpayment, so the loan amount will be 80% of the purchase price. You are talking to a lender about a 4.0% interest rate loan for 30 years that amortizes monthly. What is your monthly debt service?

Note: use the constant chart

Show how you calculated debt service in the previous question.

Now assume that property taxes are $2,400 per year and insurance is $60 per month. Based on these assumptions and the debt service you calculated in the previous question, what is your total monthly PITI?

Show your calculations below.

Based on what you can afford and the PITI you calculated for this home from the previous questions, will the bank make you this loan? Why or why not?

Please explain and show the math that led you to this conclusion.

Answer 1

Solution:

Calculation of monthly debt service

[Principal + interest] / month

Monthly payment = P[(1 + r)ⁿ * r] / (1 + r)ⁿ - 1

Where;

P = $315,100 * 0.8 = $252,080

That’s (0.28 - 0.20) = 0.8

r = 4.0% / 12 = 0.00333

n = 30 * 12 = 360

Monthly pay = $252,080[(1 + 0.00333)³⁶⁰ * 0.00333] / [(1 + 0.00333)³⁶⁰ - 1]

Monthly Debt Service = $1,202.887

Calculation of total monthly PITI

Taxes = $200 per month (2400/12)

Insurance = $60 per month

PITI = Monthly Payment + Taxes + Insurance

        = $1,202.887 + $200 + $60 = $1,462.887

House Expenses Ratio = 28% * $5,450 = $1,526

Bank will grant the loan because PITI is below the house expense ratio: $1,462.887 < $1,526