Question

Given the adjustable rate mortgage with the following characteristics:

Maturity	360
Amount borrowed	100000
Rate	LIBOR + 2% ,resets annually

At the time the issuer takes out the mortgage, LIBOR=2%. A year later on a mortgage re-set date
LIBOR=3%.

1.What is the original monthly payment on the mortgage?

2.What is the monthly payment on the mortgage after the rate changes and the mortgage is recast (i.e. in month 13)?

Answer 1

1. the original monthly payment on the mortgage is $477.42.

Loan amount	$100,000
Annual interest rate	4.00%
Loan term in months	360
No. of payments in a year	12
Monthly payment	$477.42

We need to calculate monthly payments. so, we need to use monthly interest rate and maturity in months. monthly interest rate would be: annual interest rate/12 = 4%/12 = 0.3333%.

Formula and calculations

2. the monthly payment of $447.42 includes some portion for interest and some for principal repayment. so, after one year original principal will get reduced.

hence, first we need to calculate remaining principal balance after one year or end of 12 months.

Total principal paid in 12 month is $1,761.04.

Loan amount	$100,000
Annual interest rate	4.00%
Loan term in months	360
No. of payments in a year	12
Starting month	1
Ending month	12
Total principal paid	($1,761.04)

formula will show Total principal paid as negative value because it's a cash outflow.

Formula and calculations

remaining principal balance = original principal - Total principal paid in one year = $100,000 - $1,761.04 = $98,238.96‬

now we can calculate monthly payment for month 13.

the monthly payment on the mortgage after the rate changes and the mortgage is recast is $527.37.

Loan amount	$98,238.96
Annual interest rate	5.00%
Loan term in months	360
No. of payments in a year	12
monthly payment	$527.37

Formula and calculations