The second reader understands something that eludes the first reader: that the repayment of principal on a mortgage is an investment that yields a return that is related to the cost of the mortgage.
Suppose, for example, you add $100 to the scheduled mortgage payment. This makes the loan balance at the end of the month $100 less than it would have been without the extra payment. In the months that follow, you save the interest on that $100 that you otherwise would have paid. Since the interest payment that you would have made is determined by the interest rate on your mortgage, the yield on your $100 investment is equal to that rate. The rule is that, absent any prepayment penalty, principal repayment yields a return equal to the interest rate on the loan. A prepayment penalty would reduce that yield.
To determine whether paying more principal is a good investment, the yield on this investment should be compared to the yield on alternative investments. For the first reader, the alternative yield is the 3% paid by the bank. Since the mortgage rate is 7 5/8%, this is a no-brainer. Using the money to repay principal rather than putting it in the bank will pay off the loan sooner.
The second reader, while understanding the investment rule, is off base in suggesting that the yield earned on money invested in loan repayment equals the APR. The APR usually exceeds the interest rate because of fees paid by the borrower at the time the loan was closed. But once paid, these fees are gone forever. Since they are not recoverable when principal is repaid, they don't affect the yield on principal repayment. The yield on money used to repay additional principal is the mortgage interest rate.
Postscript
Since writing the above, I have received numerous letters asking whether the yield on mortgage repayment should not be reduced by the amount of the tax saving that is lost? The answer is that if the yield on mortgage repayment is being compared to the yield on other taxable investments, it doesn't matter whether yield is measured before tax or after tax.
For example, the mortgage has a rate of 8% and it is being compared to a taxable bond paying 6%. If the tax rate is 36%, the after-tax yields are 5.12% on mortgage repayment and 3.84% on the bonds. [I calculated these by multiplying the before-tax yields by (1 - .36)]. The conclusion, that mortgage repayment earns the higher return, holds as before.
The story is different if the bond is tax exempt, however. Then I must compare the after-tax yield of 5.12% on mortgage repayment with the after-tax-yield of the bond, which is the same as the before-tax yield, or 6%. The conclusion would be reversed.
