Question

6. Jim has an annual income of $240,000. 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

Annual gross income            : $ 2,40,000

Monthly gross income          : $ 2,40,000 /12 =     $20,000

Monthly liabilities                : 140+70+178 =         $ 388            

(ie. Total of property taxes ,homeowner’s insurance, student loan payments)

Front end DTI                         : 28%

(Debt to income ratio)

Back end DTI limit                 : 36%

Maximum monthly housing payment : 28/100*20000 =5600 (ie.  Front end DTI *  Monthly gross income)

Total monthly liabilities : $ 5600+ $ 388 = $ 5988

The biggest loan Jim can get :

Present value annuity factor of monthly payment of $5600 for 30 years @ 4.5%

= $5600 *30 * 12 ( 1 -   (1+4.5% )-30

                          

                               (4.5%)

= $ 3,28,38,399.305286