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 5% annual payment cap. On the reset date, the composite rate is 6%. What would the Year 3 monthly payment be?

a. $955
b. $1,067
c. $1,003
d. $1,186
e. Because of the payment cap, the payment would not change.

Answer 1

1003

Step-by-step explanation:

Given:

Period= 30 years, Loan amount= $200,000,

Payments- Monthly,

Teaser rate for first 2 years = 4%,

Annual payment cap=5%, Composite rate on reset date= 6%

Annual rate for 2 years =4%

Monthly rate will be 4/12 = 0.3333% = 0.003333

n=30years=360 months

Monthly payment for first 2 years =
`Pr(1+r)^n/((1+r)^n-1)`

=
`200000*0.0033*1.033^(360)/(1.033^(360)-1)`

= 954.83

or by Excel function = PMT(0.003333,360,200000,0) = 954.83

Loan balance after 2 years = PV(0.003333,336,-954.83,0) = 192,812.36 or

Balance=
`A(1+r)^n-PMT*(1+r)^n-1)/i`

=
`200000(1.0033)^(24)-954.83(1+0.003333)^(24)-1)/0.003333`

= 192,812.36

Composite rate is 6% but payment is capped at 5%. So new payment from year 3 is 954.83×1.05=1002.57=1003