Question

Jim has an annual income of $300,000. 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?

How would this be calculated on a financial calculator, BA II?

Answer 1

Annual income = $300000

Monthly income = Annual income / 12 = 300000 / 12 = 25000

First we will find the Maximum monthly mortgage payment using Max front end DTI

Max front end DTI = 28%

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

Considering Maximum front end DTI

So 28% = Maximum monthly Mortgage payment + 140 + 70 / 25000

25000 x 28% = Maximum monthly Mortgage payment + 140 + 70

7000 = Maximum monthly Mortgage payment + 140 + 70

Maximum monthly Mortgage payment = 7000 - 140 - 70

Maximum monthly mortgage payment = 6790

Now we will find the Maximum monthly mortgage payment using Maximum back end DTI

max back end DTI = 36%

Back end DTI = Mortgage monthly payment + monthly homeowner's insurance + monthly property taxes + Student Loan / Monthly income

Now considering maximum back end DTI

36% = Maximum monthly Mortgage payment + 140 + 70 + 178 / 25000

25000 x 36% = Maximum monthly mortgage payment + 388

9000 = Maximum monthly mortgage payment + 388

Maximum monthly mortgage payment = 9000 - 388 = 8612

If we take Maximum monthly mortgage payment of 8612 according to max back end DTI then front end DTI limit of would be breached as Front end DTI will become 35.28%   [ (8612 + 140 +70 ) / 25000 = 35.28% ] which is greater than max front end DTI of 28%. On the other if we Maximum monthly mortgage of 6790 according to max front end DTI then our back end DTI limit would not be breached as back end DTI will become 28.71% [ (6790 + 140 + 70 +178) / 25000 = 28.71% ] which is smaller than max back end DTI of 36%. Thus any monthly mortgage payment above 6790 will breach front end DTI.

Since both the limits need to satisfied hence Maximum monthly mortgage payment = 6790

Annual rate on mortgage = 4.5%, Period of Loan = N = 30 x 12 = 360

Monthly rate = I/Y = Annual rate / 12 = 4.5% / 12 = 0.375%

PMT = Maximum monthly mortgage payment = -6790               (- sign for opposite cash flow)

To find the biggest loan Jim can get we will use pv function in ba II calculator. In ba ii calculator we enter

N=360, I/Y=0.375%, PMT = -6790 , FV = 0

then compute PV by pressing CPT and then PV

We get PV = 1340082.27

Biggest loan Jim can get = 1340082.27

.