Question

Tim wants to buy an apartment that costs $750,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.75% and monthly payments. The reset margin on the loan is 300 basis points above 1 year CMT. The index was 1% at the time of origination. Tim also had to pay 3 points for this loan. Suppose the index rate will remain 1% for the life of the loan. Compute the true APR for this loan.

Answer 1

Sol:

Apartment cost = $750,000

LTV = 85%   

Loan value (PV) = 750,000 * 85% = $637,500

Period (NPER) = 30 years, Monthly periods = 30* 12 = 360

3/1 ARM with an initial teaser rate of 3.75%, Monthly = 3.75 / 12 = 0.3125%

Reset margin on the loan = 300 basis points above 1 year CMT

To Compute the true APR for this loan.

First we have to compute monthly payments for first 3 years using PMT function, after that we have to find present value (PV) after 3 years, then again monthly payment after 3 years to get IRR.

PV	-637,500
NPER	360
Interest rate	0.3125%
Monthly payment	$2,952.36
Monthly payment	$2,952.36
NPER	324
Interest rate	0.3125%
Present value	$600,974.67
Present value	$600,974.67
NPER	324
Interest rate	0.3333%
Monthly payment	$3,036.17
Cash flow at year 0 (CF0) = Loan value - fees	631125
Cash flow for 36 months (CF1)	-2952.36
Cash flow for 324 months (CF2)	-3036.17
IRR, CPT function*12	4.03%

Working