A man is considering refinancing his existing mortgage, on which he has just mad
ID: 2669121 • Letter: A
Question
A man is considering refinancing his existing mortgage, on which he has just made his 24th payment. The rate on this 30- mortgage is 5%, and the original loan amount was $200,000 (i.e., 2 years ago he took out a $200,000, 30-year mortgage at 5%). Paul has been told he can get a new 30-year loan at 4%, and will borrow enough to (i) pay off his existing mortgage, and (ii) cover the $3,000 in closing costs for the new mortgage.Paul plans to sell his house in 3 years and to move out of the country to pursue his musical career. He believes he will be able to sell his house at that point in time for $250,000. Paul has an investment account valued at $100,000, which will earn 6% into the future.
Do you recommend that he refinance or that he simply stick with his current mortgage? Justify your recommendation (with calculated figures).
Base your decision on Paul’s expected financial situation three years from now. I.e., you should recommend whichever course of action leaves him better-off (financially) in the future.
Explanation / Answer
First find his current monthly payment: 360 N, 5/12 i, -200,000 PV, 0 FV solve for pmt = $1,073.64 Now 24 payments later he has 336 payments remaining, solve for the present value of the loan. 336 N, 5/12 i, 0 FV, 1073.64 pmt, solve for PV = 193,947.57 So he would have to borrow 193,947.57 + 3,000 for the new loan. Find the payments on the new loan. 360 N, 4/12 I, -196,947.57 PV, 0 FV solve for pmt = 940.25 Find the present value of the loans in 3 (36 payments later) years since he can invest at 6% we will use that as the discount rate for both loans. 5% loan: 300 N, 6/12 i, 0 FV, 1073.64 pmt solve for PV = 166,636.29 4% loan: 324 N, 6/12 i, 0 FV, 940.25 PMT, solve for PV = 150,685.88 Paul should elect to refinance because it will leave him ~$16,000 better off 3 years from now.
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