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 4.875%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. Tim anticipates the index to be 3.50% at the time of the 1st reset. What is Tim’s monthly mortgage payment going to be during the 1st 3 years?

A 3/1 adjustable rate mortgage (ARM) means that the monthly payment will be fixed during the first 3 years only. Then they should vary, although the variance is generally upwards. The monthly interest can be calculated by using the present value of an annuity formula:

monthly payment = present value of the loan / annuity factor

present value of the loan = $2,225,000 x 85% = $1,891,250
PV annuity factor, 0.40625%, 360 periods = 188.9615

monthly payment = $1,891,250 / 188.9615 = $10,008.65256 ≈ $10,009

suchetasVT suchetasVT · Answer 2 · 2022-03-24T14:00:58+01:00

Tim's monthly mortgage payment during the first 3 years will be $10,009 (rounded to nearest dollar).

What is an Adjustable-rate mortgage (ARM)?

A 3/1 Adjustable-rate mortgage (ARM) is a home loan with a variable interest rate. With an ARM, the initial interest rate is fixed for a period of time. Thereafter, the interest rate used on the remaining balance is adjusted periodically, annually, or monthly.

The monthly interest can be calculated by using the present value of an annuity formula:

[tex]\rm\,Monthly payment = \dfrac{Present \;Value \; of \;the \; loan}{Annuity \; \;factor}\\\\Present Value of the Loan = \$2,225,000 \times 85\% = \$1,891,250\\\\\rm\,(PV\; annuity \;factor, 0.40625\%, 360 \;Periods) = 188.9615\\\\\rm\,Monthly \;Payment = \dfrac{\$1,891,250}{188.9615} \\\\Monthly \;Payment = \$10,008.65256 \\\\Monthly \; Payment = \$10,009[/tex]

Hence, Tim's monthly payment for the first three years will be $10,009.

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