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KeithS
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Basically, the easiest way to do this is to chart out the "what-ifs".

Applying the amortization formula (see here) using the numbers you supplied and a little guesswork, I calculated an interest rate of 3.75% (which is good) and that you've already made 17 semi-monthly payments (8 and a half months' worth) of $680.04, out of a 30-year, 720-payment loan term. These are the numbers I will use.

Let's now suppose that tomorrow, you found $100 extra every two weeks in your budget, and decided to put it toward your mortgage starting with the next payment. That makes the biweekly payments $780 each. You would pay off the mortgage in 23 years (making 557 more payments instead of 703 more). The total amount of all your payments would become $434,460, down from $478,040, a savings of $43,580 in interest over the life of the loan. You also then have $780 extra every two weeks for the remaining 73 months of your original 30-year loan (a total of $56,940) which you can now do something else with. If you stuffed it in your mattress, at the end of the 30 years you'd have saved a total of $100,520).

For anything else to be worth it, you must be getting a rate of return such that $100 payments, 24 times a year for a total of 703 payments must equal $100,520. That's actually pretty easy; we use the future value annuity formula (here): v = p*((i+1)n-1)/i, plugging in v ($100520, our FV goal), $100 for P (the monthly payment) and 703 for n (total number of payments. We're looking for i, the interest rate. We're making 14 payments per year, so the value of i we find will be 1/24 of the stated annual interest rate of any account you put it into. We find that in order to make the same amount of money on an annuity that you save by paying off the loan, the interest rate on the account must average 2%. That's pretty easy; buy some corporate bonds or a long-term CD and you can beat that rate even in this economy.

However, you're probably not going to stuff the savings from the mortgage in your mattress. What if you invest it, in the same security you're considering now? That would be 146 payments of $780 into an interest-bearing account, plus the interest savings. Now, the interest rate on the security must be greater, because you're not only saving money on the mortgage, you're making money on the savings. Assuming the annuity APRs are the same, we find that the APR on the annuity must be 5.65% or better in order for paying the extra to the annuity instead of the mortgage to be the better deal.

Why is that? Because on the mortgage, you're paying a lot of interest up front on a much bigger principal than you ever contribute to the annuity, and thus losing more money to the loan than you gain in annuity earnings. So, the annuity must have a higher rate in order for the annuity's interest to catch up.

One more thing. If you live in the United States, the interest charges on your mortgage are tax-deductible. So, that $43,580 you saved by paying down the mortgage? Take 25% of it and throw it away as taxes (assuming you're in the most common wage-earner tax bracket). That's $10895 in potential tax savings that you don't get, so total savings on the loan interest is only $32685. If you penalize the "pay-off-early" track with the extra $10 grand in taxes, you find that the break-even APR on the annuity account is 5.25%.

KeithS
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