Question

Assuming a 5/1 ARM, calculate the monthly mortgage payment on a 30 year $200,000 mortgage with an initial rate of 2.75%, a rate of 4% at the time of the first adjustment, a rate of 5% at second adjustment and a rate of 4% at the third adjustment.

Answer 1

Adjustable Rate Mortgage (ARM) = 5/1 (this means that the rate will be fixed for 5 years and after which interest rate will be adjusted annually)

Mortgage period (in years) = 30

Mortgage Value = $200,000

Initial rate for 5 years = 2.75%

First adjustment rate = 4%

Second adjustment rate = 5%

Third adjustment rate = 4%

Number of adjustments after year 5 = 3

Number of months left after year 5 (30 years - 5 years) * 12 months = 300 months

Thus, it is assumed that interest rate changes once in 100 months (300/3) and in between months it remains the same as last adjustment.

Thus, interest for first 5 years or 60 months - 2.75%

Interest rate for next 100 months (month 61-160) - 4% (1st adjustment)

Interest rate for next 100 months (month 161-260) - 5% (2nd adjustment)

Interest rate for next 100 months (month 261-360) - 4% (3rd adjustment)

Calculation of monthly payments:

1. Monthly mortgage payment of 1st 5 years =

= PMT(2.75%/12,30*12,-$200,000) = $816.48

2. Monthly mortgage payment of next 100 months (month 61-160)=

Number of years loan outstanding after 5 years = 30 - 5 = 25 years

Mortgage Value outstanding at the end of 5 years (60th month) =

=PV(2.75%/12,25*12,-$816.48) = $176,991.79

Monthly mortgage payment for months 61 to 160 =

=PMT(4%/12,25*12,-$176.991.79)=$934.23

3. Monthly mortgage payment of next 100 months (month 161-260)=

Number of years loan outstanding after 160 months = (30 years * 12 months)-160 months = 200 months

Mortgage Value outstanding at the end of 160th month =

=PV(4%/12,200,-$934.23) = $136,214.17

Monthly mortgage payment for months 161 to 260 =

=PMT(5%/12,200,-$136.214.17)=$1,005.15

4. Monthly mortgage payment of next 100 months (month 261-360)=

Number of years loan outstanding after 260 months = (30 years * 12 months)-260 months = 100 months

Mortgage Value outstanding at the end of 260th month =

=PV(5%/12,100,-$1005.15) = $82,066.05

Monthly mortgage payment for months 261 to 360 =

=PMT(4%/12,100,-$82,066.05)=$966.38