. 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.
Apple Bank allows a maximum LTV of 80%.
How much is the most expensive house Jim can buy?
Maximum front end DTI limit is 28%.
Front end DTI = (monthly mortgage payment + monthly tax + monthly insurance) / monthly gross income.
28% = (monthly mortgage payment + $140 + $70) / ($300,000 / 12)
monthly mortgage payment = $6790.
Maximum back end DTI is 36%.
Back end DTI = (monthly mortgage payment + monthly tax + monthly insurance + other debt payments) / monthly gross income.
36% = (monthly mortgage payment + $140 + $70 + $178) / ($300,000 / 12)
monthly mortgage payment = $8612.
The maximum monthly mortgage payment to satisfy both ratios is $6790 (lower of the two).
With a monthly mortgage payment of $6790, the loan amount is calculated using PV function in Excel :
rate = 4.5% / 12 (converting annual rate into monthly rate)
nper = 30 * 12 (30 year loan with 12 monthly payments each year)
pmt = -6790 (Monthly payment. This is entered with a negative sign because it is a cash outflow)
PV is calculated to be $1,340,082.
The maximum loan is $1,340,082.
The maximum LTV is 80%.
LTV = loan amount / value of house
Maximum value of house = $1,340,082 / 80%
Maximum value of house = $1,675,103
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