When you purchased your home, you took out a fully amortizing mortgage for $250,000 with a...

When you purchased your home, you took out a fully amortizing mortgage for $250,000 with a 6.5% rate for a 30-year term. After 10 years, you have a chance to refinance for the remaining 20 years with a rate of 4.5%, fully amortizing over the remaining 20 years; however, you have to pay $4,500 up front for the new loan. Based on the fee and how much you will be saving per month, what is the effective annualized return (RATE calc in Excel) on the $4,500 fee paid?

a. 5.3%

b. 46.7%

c. 63.8%

d. (4.5%) negative return given monthly payment increased

Expert Solution

Monthly payment	amount borrowed/PVAF at .5416% for 360 months	250000/158.2237	1580.04
Amount borrowed		250000
PVAF at .5416% for 360 months	1-(1+r)^-n/r	1-(1.005416)^-360 / .4166%	.85694/.5416%	158.223781


remaining balance after 10 years	principal payment(1+r)^120 - monthly paymentFVAF at .5416% for 120 months	250000(1.0054)^120 -(1580.4167.7221)		212027.928
FVAF at .5416% for 120 months	(1+r)^n-1/ r	(1.0054)^120 -1 /.5416%	.908383/.5416%	167.72212

Monthly payment	amount left in loan/PVAF at .375% for 240 months	212027.928/158.2237	1340.05
Amount borrowed		139562.054
PVAF at .375% for 240 months	1-(1+r)^-n/r	1-(1.00375)^-240 / .375%	.5927/.375%	158.05

saving in monthly payment	1580.04-1340.05	239.99

what is the effective annualized return =Using rate function in MS excel	rate(nper,pmt,pv,fv,type) nper =240 pmt =239.99 pv =-4500 fv =0 type =0	RATE(240,239.99,-4500,0,0)	5.3%

jeff jeffy answered 2 years ago

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