Question

You and your spouse are considering purchasing a home.

The home you are purchasing is $231,250. You plan on offering full price today. You have a 10% down payment and your are financing the remaining balance for 30 years. (Round off the amount you are financing to nearest dollar.) You have checked with several lenders and find the best rate to be 4.5% for 30 years. In order to qualify for the loan the lender tells you that your front end Debt to Income ratio is to be no more than 28% and your back end Debt to Income ratio is to be no more than 36%.

Your currently have the following debts:

Truck Loan -36 months remaining - $295 a month

Car Loan – 18 months remaining- $255 a month

One Student Loan with 72 months remaining -$205 a month

Credit card debt of $65 a month

The taxes on the property are $1,800 annually

Utilities on this home average $320.00 a month

The annual insurance premium on this home would be $1,200.

You annual income is $85,000.

Front End Ratios are based on PITI- Principle, Interest, Taxes and Insurance.

Back End Ratios are based on PITI and all other monthly payments

1. What is your down payment?

2. What is your loan amount?

3. What is your monthly payment? Principal and Interest Only

4. Calculate your front-end debt to income ratio, which includes just the monthly principal and interest and taxes and insurance. (PITI)

5.Calculate your back-end debt to income ratio, which includes the monthly PITI AND all other monthly debt.

6. Do you qualify to purchase the home based on your debt to income ratios?

Answer 1

Ans 1) Down Payment = 10% of Purchasing price = 10% * 231250 = $23125

Ans 2) Loan Amount = Purchasing Price – Down Payment = 231250 – 23125 = $208,125

Ans 3) Monthly Payment = Loan amount * (i/(1-(1+i)^(-n))), i = 0.375% (=4.5%/12) & n = 360 (30*12)

Monthly Payment = 208125 * (0.375%/(1-(1+0.375%)^(-360))) = 1054.54

Ans 4) Monthly Debt Servicing (i.e. Principal + interest)

Truck Loan = $295

Car Loan = $255

Student Loan = $205

Credit Card = $65

Proposed Home Loan = $1054.54

i.e. Total = 295+255+205+65+1054.54 = $1874.54

Property Tax = $1800 annually

Insurance Premium on proposed property = $1200 annually

Front-end debt to income ratio = (1874.54*12 + 1800+1200)/85000 = 29.99%

Ans 5) Additionally, to calculate Back-end debt to income ratio, we need to include

Utilities = $320 a month

Back-end debt to income ratio = (1054.54*12+320*12+1800+1200)/85000

= 34.51%

As threshold value for front-end debt to income ratio is 28%, buyer doesn’t qualify for loan, since ratio is 29.99% which is greater than the upper threshold.

As threshold value for back-end debt to income ratio is 36%, buyer qualifies for loan, since ratio is 34.51% which is lesser than the upper threshold.

If both ratios are to be strictly complied then buyer doesn’t qualify for loan.