Question

A borrower takes out a 30-year adjustable rate mortgage loan for $200,000 with monthly payments. The first two years of the loan have a “teaser” rate of 4%, after that, the rate can reset with a 2% annual rate cap. On the reset date, the composite rate is 5%. What would the Year 3 monthly payment be?

a. $955

b. $1,071

c. $1,067

d. $1,186

e. Because of the rate cap, the payment would not change.

Answer 1

First, we calculate the monthly payment in the first two years.

Monthly loan payment is calculated using PMT function in Excel :

rate = 4% / 12   (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 200000 (loan amount)

PMT is calculated to be $954.83

А1 х v f =PMT(4%/12,30*12,200000)*-1 B C D 1 $ 954.83 |

Now, we calculate the principal paid off after 2 years (24 months) using CUMPRINC function in Excel :

rate = 4%/12 (converting annual rate into monthly rate)

nper = 30*12 (30 year loan with 12 monthly payments each year)

pv = 200000 (original loan amount)

start period = 1 (We are calculating principal paid off between 1st and 24th month)

end period = 24 (We are calculating principal paid off between 1st and 24th month)

type = 0 (each payment is made at the end of month)

CUMPRINC is calculated to be $7,187.64

The balance loan principal outstanding after 2 years =  $200,000 - $7,187.64 = $192,812.36

X Fac =CUMPRINC(4%/12,30*12,200000,1,24,0) 2 $ (7,187.64)!

On the reset date, the composite rate is 5%. The annual rate cap is 2%. This means that the rate cannot increase more than 2% above the teaser rate, which means that the rate cannot exceed 6%. As the composite rate is 5%, we use 5% as the interest rate of the loan for the third year.

We calculate the monthly payment in the third years using PMT function in Excel :

rate = 5% / 12   (converting annual rate into monthly rate)

nper = 28*12 (28 years remaining on loan with 12 monthly payments each year)

pv = 192812.36 (balance loan principal outstanding after 2 years)

PMT is calculated to be $1,067

А4 =PMT(5%/12,28*12,А3) B C D E 3 4 A $192,812.36 $ (1,067.36)!