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%. The reset margin on the loan s 300 basis points above 1 year CMT. The index was 1% at the time of origination. Tim also had to pay 3 points ifor this loan. Suppose the index rate will remain 1% for the life of the loan. Compute the true APR for this loan.

Answer 1

Loan size = 0.85* 750,000 = 637,500.

Tim’s payment for the first 3 years:

[360, N], [3.75/12, I], [637,500, PV], [CPT, PMT] PMT = $2952.36

Tim’s balance after 3 years.

[324, N], [3.75/12, I], [2952.36, PMT] , [CPT, PV] PV= $600,974.28

True APR assumes the index stays the same =1% for the life of the loan.

Hence the mortgage rate= the fully indexed rate (FIR) = fully indexed rate = index + margin

= 1%+3%= 4%.

Tim’s new payment:

[324, N], [4/12, I], [600,974.28, PV], [CPT, PMT] PMT=$3036.17

Points=3%*637,500=19,125, adjusted present value=618,375

Compute the IRR:

CF0 = 618,375

CF1=-$2952.36, F1=36

CF2=-$3036.17, F2=324

IRR,

CPT * 12 = 4.2%