Consider an adjustable rate mortgage of $90,000 with a maturity of 30 years and monthly payments. At the end of each year, the interest rate is adjusted to become two percentage points above the index. There is an annual cap of 300 basis points, and a lifetime cap of 500 basis points. In the first year the contract rate is 7%, with no teaser. In year two, the index rate is 9%. What monthly payment is called for in year two?

EMI 1st year = $598.77

EMI 2nd year = $786.11

Explanation:

given data

contract rate = 7%

PV = 90000

time period =30 year

solution

Adjustment (called margin ) is 2%.

The first step is to calculate the contract rate for the second year as there is no cap. So, 9% + 2% = 11%.

The second step is to include any barriers imposed by the annual and lifetime cap

so Annual increase in contract rate is limited to 3%. Since the first year contract rate is 7%,

The second year contract rate should not exceed 10%.

and

we get here EMI for 1st year that is

we use excel with rate 7% and PV $90,000 and time 30 year we get

EMI 1st year = $598.77

and after 1 year that principal amount left

amount left =  89080$

so with rate 10 % and time period 29 year and amount 89080

we get EMI

EMI 2nd year = $786.11