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15 year vs 30 year - Investing the difference

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Note: You can use any financial calculator to do this problem, but if you want the BEST, you can get our 10bii Financial Calculator for iOS, Android, Mac, and Windows!

THE SCENARIO I've recently written about offers I get from time to time that offer me 15-year mortgages and compare them to 30-year ones. They rightly claim that I can save thousands over the life of the loan, but I've maintained that I prefer the longer term and lower required payment of longer loans, and demonstrated that I can pay them off nearly as quickly as the shorter loans if I choose to do so. I've also said that though I'm free to pay down such loans more quickly, I generally would not do that when the interest rate on the loan is low. The primary reason for this is that once I've sent a dollar to the bank to pay down a loan, that dollar is theirs, and I can't get it back if I need it. Also, if I'm borrowing at 4.625%, then I get a guaranteed return of 4.625% on that dollar... but I think I can do better than that. What's more, if I pay down 99% of my mortgage (early, even), and then default, they get to keep all the money I've given them, and they also get to repossess the house (though in this case, that would likely just force me to sell the house, but I'd really prefer not to be forced to move). The question: Let's say I could afford the monthly payment on the 15-year mortgage ($2,275.86), but I get the 30-year mortgage instead (monthly payment of $1,542.42). Even though I got the 30-year mortgage from the bank, I'd still like to find a way to pay it off in 15 years. If I took the difference between those payments ($2,275.86 $1,542.42 = $733.44) and invested it at 9%, how much money would I have after 15 years? Could I pay off the remaining mortgage and have some bonus money left over? And if so, how much would I have left? The 30-year loan is at 4.625% interest, with $300,000 borrowed, and it amortizes fully.
THE SOLUTION To solve this one, we need to do three things:
  1. Figure out how much my investment account would be worth after 15 years
  2. Figure out what I'd still owe on my 30-year loan after 15 years
  3. Figure out how much I'd have left over after paying off my house, if any
First things first, make sure the calculator is using 12 Payments per Year. Part 1: How big does my investment get? N: 180 (I'm investing my money for 15 years, which is 180 months) I/YR: 9 (I get a 9% return on my investment) PV: 0 (I start with nothing in my investment account) PMT: -733.44 (I'm investing the $733.44 difference every month for 15 years) FV: (This is what I'm trying to find)

After 15 years, I have $277,537.93 in my investment account.

Part 2: How much will I still owe? N: 180 (I'm trying to find out how much I'll still owe after 15 years) I/YR: 4.625 (The 30-year loan's interest rate is 4.625%) PV: 300,000 (I originally borrow $300,000) PMT: -1,542.42* (I pay $1,542.42 per month on this loan) FV: (This is what I'm trying to find) * Instead of calculating this number, I type it in, since I can only pay in whole pennies. If I were to calculate it, there would be fractional cents that would throw off my results very slightly.

After 15 years of paying down my 30-year loan, I'll still owe $199,950.91. So after paying for ½ the total time in the loan, I've only paid off ⅓ of the balance. There's a lesson in there somewhere...

Part 3: How much will I have left over?

If I use my investment account to pay off my mortgage, then I have a free-and-clear house (the mortgage has been paid off, or 'satisfied'), as well as $277,537.93 - $199,950.91 = $77,587.02.

If I'd have gotten the 15-year loan, I'd still have a free-and-clear house, but I wouldn't have the extra $77K. Also, if I'd hit an income interruption during those 15 years, I may have lost the house rather than missing some contributions to my investing account. Because my investment account yields such a higher rate than I'm paying on the mortgage, I still end up with a healthy account after paying off the loan. Remember that my monthly outflow during the 15 years is the same as it would have been if I'd taken the 15-year loan, but I was able to make all that extra money while simultaneously maintaining the flexibility to more easily weather financial issues that may arise during that 15 years.

What do you think? Would you prefer the get-the-30-year-invest-the-difference approach, or do you think that just getting the 15-year loan would work better for you? Would you, after the 15 years is over, actually take the step of paying off your house? Do you have other ideas on the topic? Let us know in the comments!