FreddieMac reports that the average rate on a 30-year fixed rate mortgage is 3.9

Question

FreddieMac reports that the average rate on a 30-year fixed rate mortgage is 3.92% as of January 2012. This is down from 4.76% in January 2011 and 5.03% in January 2010. If you have a $218,000, 5%, 30-year mortgage, how much interest will you save if you refinance your loan at 3.5% for 20 years? (Use 360 days a year. Round your answer to the nearest cent.)

FreddieMac reports that the average rate on a 30-year fixed rate mortgage is 3.92% as of January 2012. This is down from 4.76% in January 2011 and 5.03% in January 2010. If you have a $218,000, 5%, 30-year mortgage, how much interest will you save if you refinance your loan at 3.5% for 20 years? (Use 360 days a year. Round your answer to the nearest cent.)

Explanation / Answer

TOtal Interest paid for the life of mortgage is given by,

=MP*T-MB0

MB0=Loan AMount=218,000

T=maturity=30 years,MP=monthly pay

Let MB0=Loan AMount=218,000, MP=monthly pay=?, r be the current market rate of interest=5% or 5/12%=.0.41666667% per month, T be time to maturity=30*12=360 months

MP=(MB0*r)/(1-1/(1+r)T)

MP=(218,000*.0041666667)/(1-1/(1.0041666667)360)

MP=1170.27114

Thus TOtal Interest paid for the life of 5%, 30-year mortgage=1170.27114*360-218,000=203297.6104

3.5% ,20 -year mortgage

Let MB0=Loan AMount=218,000, MP=monthly pay=?, r be the current market rate of interest=3.5% or 3.5/12%=0.291666667% per month, T be time to maturity=20*12=240 months

MP=(MB0*r)/(1-1/(1+r)T)

MP=(218,000*0.00291666667)/(1-1/(1.00291666667)240)

MP=1264.312186

Thus TOtal Interest paid for the life of 3.5%, 20-year mortgage=1264.312186*240-218,000=85434.92464

Interest savings= TOtal Interest paid for the life of 5%, 30-year mortgage-TOtal Interest paid for the life of 3.5%, 20-year mortgage

Interest savings= 203297.6104-85434.92464=117862.68576

Interest savings=$ 117,862.69

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