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How Much Did They Owe?

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THE SCENARIO Last time, I talked about a loan I was looking at recently. It's got a current balance of $198,984.80, a monthly P&I (Principal and Interest) payment of $1050.31, and has received 60 payments so far from the borrower. Its interest rate, as determined last time, is 4.00%. The question: What was the original balance of the loan?
THE SOLUTION This is very straightforward. We already have every piece of information we need to solve it. First things first, make sure the calculator is using 12 Payments per Year. N: 60 (The borrower has paid 60 payments on the loan) I/YR: 4.00 (The interest rate on the loan is 4.00%) PV: (This is what I'm trying to find) PMT: -1,050.31 (The monthly P&I payment is $1,050.31) FV: -198,984.80 (The borrower owes $198,984.80 today)

The borrower originally borrowed $220,000.22.

It's likely that the $0.22 is a rounding error and that they really borrowed an even $220K. These can happen because the actual payment should be $1,050.313650024 each month (or something similar)... but we can't pay fractional pennies, so we round to the nearest (or next-highest) penny. Over the course of many months, the extra fractions of a penny add up, throwing off the totals ever-so-slightly. In the end, the differences usually end up being so tiny as to not be worth stressing over.

What do you think? Did you notice that over 16.67% of the time (5 years out of 30), only 9.55% of the money ($21K of $220K) has been repaid? What lessons can you take from that piece of knowledge? Let us know in the comments!