Question

6. Jim has an annual income of $180,000. Jim is looking to buy a house with monthly property taxes of $140 and monthly homeowner’s insurance of $70.

Jim has $178 in monthly student loan payments.

Apple bank has a maximum front end DTI limit of 28% and a maximum back end DTI limit of 36%. Both limits must be satisfied.

Apple bank is offering a fully amortizing 30 year FRM at an annual rate of 4.5%, with monthly payments, compounded monthly. What is the biggest loan Jim can get?

Answer 1

Monthly income = Annual income / 12 = 180000 / 12 = $15000

We know that Front end DTI is percentage of monthly income that goes towards home loan expenses.

where home loan expenses = Monthly loan payment + monthly property taxes + monthly homeowner's insurance

Front end DTI = ( Monthly loan payment + monthly property taxes + monthly homeowner's insurance) / Monthly income

For maximum Front end DTI = 28%

Maximum Front end DTI = (Maximum Monthly loan payment + monthly property taxes + monthly homeowner's insurance) / Monthly income

28% = (Maximum Monthly loan payment + 140 + 70) / 15000

15000 x 28% = Maximum Monthly loan payment + 140 + 70

4200 = Maximum Monthly loan payment + 140 + 70

Maximum Monthly loan payment = 4200 - 210 = 3990

Using Front end DTI we get maximum monthly loan payment = $3990

We know that Back end DTI is percentage of monthly income that goes towards debt obligations

where monthly debt obligations = monthly home loan expenses + monthly student loan = Monthly loan payment + monthly property taxes + monthly homeowner's insurance + monthly student loan

Back end DTI = ( Monthly loan payment + monthly property taxes + monthly homeowner's insurance + Monthly Student loan) / Monthly income

For maximum Back end DTI = 36%

Maximum Back end DTI = (Maximum Monthly loan payment + monthly property taxes + monthly homeowner's insurance + Monthly Student loan) / Monthly income

36% = (Maximum Monthly loan payment + 140 + 70 + 178) / 15000

15000 x 36% = Maximum Monthly loan payment + 140 + 70 + 178

5400 = Maximum Monthly loan payment + 140 + 70 + 178

Maximum monthly loan payment = 5400 - 140 - 70 - 178 = 5012

Using Back end DTI,we get maximum monthly loan payment = $5012

If we take maximum monthly payment equal to $3990(on the basis of max front end DTI), then front end DTI will be equal to 28% and back end end DTI will be equal to = 29.18% [ (3990 + 140 + 70 + 178 ) / 15000 = 4378 / 150000 = 29.19%.]. So both the DTIs will be within the prescribed limits.

If we take we take maximum monthly payment equal to $5012 (on the basis of max back end DTI), then back end DTI will be equal to 36% but front end end DTI will be equal to = 34.81% [(5012 + 140 + 70) / 15000 = 5222 / 15000 = 34.81%. So this monthly payment will lead to front end DTI exceed maximum prescribed limit of 28%

So we infer that maximum monthly loan payment cannot exceed $3990. Hence Maximum monthly loan payment = $3990

Period of loan = 30 years = 12 x 30 months = 360 months

Monthly rate = Annual rate / 12 = 4.5% /12

Using maximum monthly loan payment, we can find the maximum loan Jim can get. We will use PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel, we get maximum loan payment Jim can get = $787471.0244 = $787471.02

Biggest loan Jim can get = $787471.02