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## Paying Less on the Mortgage

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!
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THE SCENARIO A \$100,000 mortgage at 6% for 30 years has a monthly payment of \$599.55. However, let's say that you want to borrow the same money at the same rate, but you only have \$475 per month to spend. You're willing to keep paying for longer than 30 years though. The question: How long does it take to pay off the loan?
THE SOLUTION This one looks straightforward on its face... but it's a little less simple than it seems. First things first, make sure the calculator is using 12 Payments per Year. N: (This is what I'm trying to find) I/YR: 6 (The interest rate is 6% per year) PV: 100,000 (The initial loan balance is \$100,000) PMT: -475 (The payment is \$475 per month) FV: 0 (The loan amortizes fully)

This question has No solution.

Huh? I thought calculators could calculate things! What do you mean there's no solution, why do I even have this app if it can't calculate the answers to problems for me? Well, the reason the calculator can't find a solution to the problem is that there legitimately is no solution. Let's take a moment to figure out why. If the loan were interest only, the payment would be \$100,000 x 6% = \$6,000 per year. This amounts to \$6,000 ÷ 12 = \$500 per month just in interest. Do you see the issue yet? If the first month's accrued interest is \$500, and the payment is only \$475, that means that the payment doesn't even cover the interest (it's \$25 short), and the balance actually rises from one month to the next. What's worse, month 2 is even farther behind than month 1, because the balance owed is \$100,025, and the interest on that amount is actually higher than on a flat \$100k (\$500.13, to be exact). That means that month two ends with the borrower even deeper in the hole than they were after month one, and so on down the line. Simply put, the loan never gets paid off, and the balance owed increases over time, faster and faster, higher and higher.

What do you think? Does this explanation make sense to you? How can you use the knowledge of the potential for rising balances to inform your borrowing and investing decisions? Let us know in the comments!