For Problems 611 assume you buy a ho for 30 years You pay a

For Problems 6-11, assume you buy a ho for 30 years. You pay a total of $7,825 for origination fee, points, and mortgagè insurance. In addition, you pay other loan costs of $1,685. You pay the first year\'s hazard insurance premium of $475 and are required to deposit $380 into an escrow account. 30 X l a-3 (o 0 me ana boTTOW STOU,00o ao 6. What is the reportable APR?

Solution

Mortgage Loan Amount given is $150,000 and interest rate is 4.96%. The monthly mortgage payment for 30 year loan tenure will be given by formula:

Monthly Payment = Loan AMount * [ r * (1+r)^t ] / [ (1+r)^t - 1 ] ; where r is the monthly interest rate and t is tenure in months. Plugging in the values we get:

Monthly mortgage payment = 150000 * [ (4.96%/12) * (1 + 4.96%/12)³⁶⁰ ] / [ (1 + 4.96%/12)³⁶⁰ - 1 ] = 801.57

Now the total fees and other expenses paid are = 7825 + 1685 + 475 + 380 = 10365

Hence the net loan amount shall be (150000 - 10365) = 139635

Now the effective APR for this loan shall be the discount rate which will equate the monthly mortgage payments to the net loan amount, as below:

139635 = 801.57/(1+r) + 801.57/(1+r)² + ....... + (801.57 - 380)/(1+r)³⁶⁰

We have added 380 back in the last term since it is only being deposited in the escrow and should be returned back once the loan is repaid. SOlving for r we get, r = 0.47% monthly or annualised 5.59%