I have a mortgage of 30 yrs amortization and have 290k left on the mortgage. It suddenly hit me that with my bi weekly payment of 620, it would take forever to pay it off. I need some help deciding if when i have some 'disposable' income, i should pay toward mortgage or i should pay towards a high value savings account. In other words, how to decide between paying off mortgage and investing in high value saving account,bond etc(not stock)
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1 Answer
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 semi-monthly payments $780 each. You would pay off the mortgage in 23 years (making 557 more payments instead of 703 more). Your total payments will be $434,460, down from $478.040, so your interest costs on the loan were reduced by $43,580 (but, my mistake, we can't count this amount as money in the bank; it's included in the next amount of money to come in). Now, after the mortgage is paid off, you have $780 semi-monthly for the remaining 73 months of your original 30-year loan (a total of $113,880) which you can now do something else with. If you stuffed it in your mattress, you'd earn 0% and so that's the worst-case scenario.
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 $113,880. We use the future value annuity formula (here): v = p*((i+1)n-1)/i, plugging in v ($113880, 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 24 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 3.07%.
However, you're probably not going to stuff the savings from the mortgage in your mattress and sleep on it for 6 years. 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 APR stays the same now vs later, we find that the APR on the annuity must equal, surprise, 3.75% in order to end up with the same amount of money.
Why is that? Well, the interest growing on your $100 semi-monthly exactly offsets the interest you would save on the mortgage by reducing the principal by $100. Both the loan balance you would remove and the annuity balance you increase would accrue the same interest over the same time if they had the same rate. The main difference, to you, is that by paying into the annuity now, you have cash now; by paying into the mortgage now, you don't have money now, but you have WAY more money later. The actual real time-values of the money, however, are the same; the future value of $200/mo for 30 years is equal to $0/mo for 24 years and then $1560/mo for 6 years, but the real money paid in over 30 years is $72,000 vs $112,320. That kind of math is why analysts encourage people to start retirement saving early.
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 over the life of the loan. If you penalize the "pay-off-early" track by subtracting those extra taxes, you find that the break-even APR on the annuity account is about 3.095%.
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4Keith - if the rate of the mortgage is 3.75%, then that's the rate he'd need from a side savings account. Any suggestion that mortgages are frontloaded only obfuscates the real math. Interest accrues on the balance owed, not much more complicated than that. Commented Aug 2, 2012 at 1:59
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Thanks for your detailed answer. I think I need to read it a few times as i am pretty green in this area :) Commented Aug 2, 2012 at 2:22
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2The first thing that occurs to me is that the OPs payments are biweekly, i.e. every two weeks or about 26 payments per year, not the 24 you mention. All I know is that tax math aside, investing the extra payments at the same rate as the mortgage produces the same result as prepaying the mortgage, to me it's a fact requiring no proof. Where thing take a turn is if OP were considering an investment that was tax favored, either dividends or cap gains, while his mortgage is benefiting at his marginal rate. But he said not to look at stocks, so I didn't. The biweekly vs semimonthly will trip you up Commented Aug 2, 2012 at 20:02
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1However, another look at the numbers says you're right. I was double-counting interest savings; the money you save in interest by paying early comes in the form of $680 semi-monthly for 73 months. If you then invest that as an annuity for 73 months at 3.75% you get just a couple dollars more than taking the $100 and stuffing it in an annuity for the remaining full life of the loan (and that gain is probably a rounding error). Subtract extra taxes you owe because you can't deduct your interest savings, and the breakeven becomes just a little more than 3%. I will edit.– KeithSCommented Aug 2, 2012 at 22:04
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1I wouldn't consider the marginal tax rate against the entire interest paid as benefit, since mortgage interest is what pushes many people into itemizing deductions. The benefit over standard deduction can be pretty negligible or non-existent for many home owners. I've only seen a handful of returns where there was benefit from itemizing without mortgage interest, in the vast majority only a fraction of the interest was providing tax benefit.– Hart COCommented Nov 24, 2017 at 15:46
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