Question

You borrow a GPM (graduate payment mortgage) of $10,000 with annual payments and 3-year term. The interest rate is 10% with $100 origination cost. The payment factors from year 1 to year 3 are as follows: 25%, 50% and 100% What is the annual payment in the 1st year?

$1,796.22

$3,592.44

$7,184.89

$1,005.29

What is the effective cost of this loan if you holding the loan for 3 years?

10.47%

10.27%

10.67%

None of the above

Answer 1

First Question:

The correct answer is the first option showing $  1,796.22

Let P be the the annual payment in the 1st year. The payment factors from year 1 to year 3 are as follows: 25%, 50% and 100%.

Hence, payment in year 2 = 2 times the payment in year 1 (Payment factor of year 2 is 50% which is two times the payment factor of 25% in year 1) = 2P

Payment in year 3 = 4 times payment in year 1 ((Payment factor of year 3 is 100% which is four times the payment factor of 25% in year 1) = 4P

The loan today = PV of all the future payments

i = interest rate = 10%

Hence,

Hence, P = 10,000 / 5.5672 = $  1,796.22

Hence, the correct answer is the first option showing $  1,796.22

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Second Question

The correct answer is first option showing 10.47%

Effective Initial disbursement = Loan amount - origination fees = 10,000 - 100 = 9,900

Hence, series of cash flows will be like this. We have to calculate the IRR. I have done it using excel. The cell in yellow contains the answer. The cell in blue shows the excel formula.