Question

A variable rate mortgage is established for $300,000 at a margin of 1.25% above the benchmark rate of 3.75% with a term of 25 years. After one year has elapsed the benchmark rate increases to 4.25%. What is the initial monthly payment and by how much does it increase at the end of the first year?

Answer 1

Here rate = (1.25%+3.75%)/12 = 5%/12, nper = 25*12 = 300 months and PV = $300,000

Thus initial monthly payment will be = PMT(5%/12, 300, 300000) = $1,753.77

Next we will compute the amount of mortgage due after a period of 1 year (i.e 12 months).

Period	Mortgage due at the start of the month	Monthly payments	Interest	Principal repaid	Mortgage due at the end of the month
1	300,000.00	1,753.77	1,250.00	503.77	299,496.23
2	299,496.23	1,753.77	1,247.90	505.87	298,990.36
3	298,990.36	1,753.77	1,245.79	507.98	298,482.38
4	298,482.38	1,753.77	1,243.68	510.09	297,972.29
5	297,972.29	1,753.77	1,241.55	512.22	297,460.07
6	297,460.07	1,753.77	1,239.42	514.35	296,945.72
7	296,945.72	1,753.77	1,237.27	516.50	296,429.22
8	296,429.22	1,753.77	1,235.12	518.65	295,910.57
9	295,910.57	1,753.77	1,232.96	520.81	295,389.76
10	295,389.76	1,753.77	1,230.79	522.98	294,866.78
11	294,866.78	1,753.77	1,228.61	525.16	294,341.63
12	294,341.63	1,753.77	1,226.42	527.35	293,814.28
			Total	6,185.72

Thus mortgage due at the end of first year = 300,000 - 6,185.72 = $293,814.28

Interest rate now = 1.25%+4.25% = 5.50%, nper = 300-12 = 288

So monthly payment now will be = PMT(5.5%/12, 288, 293814.28) = $1,839.54

Thus the answers are:

Initial monthly payment = $1,753.77

Monthly payments after 1 year = $1,839.54

Increase = 1839.54-1753.77 = $85.77