Question

You take out a 25 year, $275, 000 mortgage with constant payments at the end of each month and i (12) = 6%. After 15 years, you wish to refinance the mortgage with a 10 year mortgage (also with constant payments at the end of each month) so that you pay $100 less each month than you originally were paying. Find the monthly nominal interest rate corresponding to this new mortgage

Answer 1

Answer :

Loan present value (PV) = $275,000

Interest rate = 6% for first 15 years, compounded monthly = 6/12 = 0.50%

Loan period [NPER] = 25 years, Monthly = 25*12 = 300

Refinance the mortgage with a 10 year mortgage, so that you pay $100 less each month

To find the monthly nominal interest rate corresponding to this new mortgage we have to use PMT, PV and RATE function in excel

PV	-275,000
NPER	300
Monthly interest rate	0.50%
Monthly payment	$1,771.83
Remaining NPER	120
PV	$159,594.74
Monthly payment	$1,671.83
Monthly interest rate	0.3942%

Therefore monthly nominal interest rate corresponding to this new mortgage will be approximately 0.39%

Working

-	A	B
1	PV	-275000
2	NPER	=25*12
3	Monthly interest rate	=6%/12
4	Montly payment	=PMT(B3,B2,B1,0)
5	-	-
6	Remaining NPER	=10*12
7	PV	=PV(B3,B6,-B4,0)
8	Monthly payment	=B4-100
9	Montly interest rate	=RATE(B6,-B8,B7,0)