A homeowner took out a 30-year, fixed-rate mortgage of $310,000. The mortgage wa
ID: 2641401 • Letter: A
Question
A homeowner took out a 30-year, fixed-rate mortgage of $310,000. The mortgage was taken out 10 years ago at a rate of 7.50 percent. If the homeowner refinances, the charges will be $2,500. What is the highest interest rate at which it would be beneficial to refinance the mortgage? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)
A homeowner took out a 30-year, fixed-rate mortgage of $310,000. The mortgage was taken out 10 years ago at a rate of 7.50 percent. If the homeowner refinances, the charges will be $2,500. What is the highest interest rate at which it would be beneficial to refinance the mortgage? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Explanation / Answer
Assuming yearly payments
step1:
calculate the amount of pricipal to be paid after 10 years , using amortization schedule of loan
so, after 10 years 267,585.86 to be paid
step2:
the homeowner will enjoy benefit if the new finance rate will take of the extra $2500 refinances charge
the yearly payment will be same
yearly payment = $26248.08
Let i be the required APR
=>
26248.08 * [1-(1+i)^-20]/i = 267,585.86 + 2500
=>
i = 7.39%
therefore the highest interest rate which will be beneficial to refinance the mortgage is 7.39%
Beginning Balance Interest Principal Ending Balance 1 $310,000.00 $23,250.00 $2,998.08 $307,001.92 2 $307,001.92 $23,025.14 $3,222.94 $303,778.98 3 $303,778.98 $22,783.42 $3,464.66 $300,314.32 4 $300,314.32 $22,523.57 $3,724.51 $296,589.81 5 $296,589.81 $22,244.24 $4,003.84 $292,585.96 6 $292,585.96 $21,943.95 $4,304.13 $288,281.83 7 $288,281.83 $21,621.14 $4,626.94 $283,654.88 8 $283,654.88 $21,274.12 $4,973.96 $278,680.91 9 $278,680.91 $20,901.07 $5,347.01 $273,333.90 10 $273,333.90 $20,500.04 $5,748.04 $267,585.86Related Questions
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