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Answer: At all times during the life of the mortgage loan, the mortgage rate is the yield to maturity (YTM) on the loan held to maturity
**Correct answer: B.** The key point is that the **yield to maturity (YTM) is not fixed over the life of a mortgage loan** because the mortgage can be prepaid and because the loan balance and term structure of interest rates change over time. In contrast: - **A is true**: the mortgage rate corresponds to the IRR on the loan if held to maturity. - **C is true**: when rates fall, the value of the borrower's liability increases, and refinancing becomes attractive when that value exceeds the remaining principal. - **D is true**: prepayment creates reinvestment risk for the bank, and the mortgage rate partly compensates for this risk. Thus, the false statement is **B**.
Author: Manit Arora
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In regard to a mortgage loan and prepayment, each of the following is true EXCEPT:
A
At all times during the life of the mortgage loan, the mortgage rate is the internal rate of return (IRR) on the loan held to maturity
B
At all times during the life of the mortgage loan, the mortgage rate is the yield to maturity (YTM) on the loan held to maturity
C
When interest rates decline, the market value of the mortgage owner's liability, , increases; if this value, , increases above the principal remaining, , it becomes advantageous for the homeowner to refinance the mortgage
D
Prepayment is costly to the bank because the bank forgoes the higher mortgage rate in favor of a lower market rate; therefore, the bank obtains partial compensation in the (higher) mortgage rate
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