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Answer: 4.29%
Set the present value of the remaining 300 monthly payments equal to the outstanding balance of $89,850 and solve for the mortgage rate. Using the annuity PV relationship: \[ PV = PMT \times \frac{1-(1+i)^{-n}}{i} \] with: - \(PV = 89{,}850\) - \(PMT = 454.65\) - \(n = 300\) months remaining - \(i = r/12\) Solving gives an annual mortgage rate of approximately **4.29%**. So refinancing becomes financially desirable when the current mortgage rate exceeds about **4.29%**.
Author: Manit Arora
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Question-509.1. After five years (60 monthly payments), the outstanding balance on a mortgage is $89,850.00 when the original balance was $100,000. The mortgage is a 30 year fixed rate mortgage (FRM) and each monthly payment is $454.65. As Tuckman explains, "The prepayment option is valuable when mortgage rates have fallen. In that case, as mentioned previously, the present value of the remaining monthly payments exceeds the principal outstanding."
If we ignore transaction costs, according to Tuckman's principle, what is the highest mortgage rate at which prepayment (for example, refinance) is financially desirable?
A
1.99%
B
2.75%
C
3.60%
D
4.29%
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