Question

8. Tim wants to buy an apartment that costs $2,225,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.75%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. The index was 1% at the time of origination. Tim also had to pay 6.5 points for this loan.

Compute the true APR (annualized IRR) for this loan.

Answer 1

Final answer: Annualized IRR = 4.50%

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Detailed solution follows:

3/1 ARM means fixed rate for first three years and variable rate from fourth year onward.

Fixed rate for first three years = initial teaser rate = 3.75%

Variable rate thereafter = 1% + margin = 1% + 300 basis points = 1% + 3% = 4%

Let's assume the index remains at 1% throughout, otherwise we will not be able to solve this question.

It involves massive calculation. I am therefore resorting to excel.

Please see the table below. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.