Given the recent drop in mortgage interest rates, you have decided to refinance

Question

Given the recent drop in mortgage interest rates, you have decided to refinance your home. Exactly 6 years ago, you obtained a $262,000.00 15-year mortgage with a fixed rate of 11% APR, compounded monthly. Today, you can get a 15-year loan for the currently outstanding loan balance at 4% interest, compounded monthly. This loan, however, requires you to pay a $250 appraisal fee and 3 points at the time of the refinancing (1 point equals 1% of the amount borrowed). Ignore tax considerations.

A. If you stay with the original loan and do not refinance, how much are your monthly payments?

B. If you refinance, how much will your new monthly payments be after you refinance?

C. Is it worth it to refinance? Explain. Your explanation should contain mathematical justification, i.e. how much would one plan save over the other plan, what is the total cost of the house, etc.

Explanation / Answer

a) Loan (Principal) $262,000.00 Rate = 11%/12 0.92% Period = 15 x 12 180 Monthly Payment = PMT(0.92%,180,-262000) $2,977.88 b) Outstanding Balance at the beginning 7 the year FV(0.92%,72,2977.88,-262000) $203,604.01 Total new borrowed Capital $203,604.01 Rate = 4%/12 0.33% Period = 15 x 12 180 Monthly Payment = PMT(0.33%,180,-203604.01) $1,506.03 c. Yes it is worth to refinance. Net savings on monthly payments = $2977.88 - $1506.03 $1,471.85 Total cost of House Old loan $203,604.01 New loan (principal + interest) = $1506.03 x 180 $271,086.17 Appraisal fee $250.00 Refinancing Fee ($203604.01 x 3%) $6,108.12 Total cost of House $481,048.30

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