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What Was It Before?

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THE SCENARIO I was having a discussion with a friend this week about a note they're considering buying. She knows the current terms of the note, and how long it's been since it was originated, but she doesn't know the original owed balance. So we'll try and help her out by determining the answer. I've changed all of the numbers for the sake of anonymity and simplicity. The question: If there are 88 monthly payments of $528.60 left to pay and $32,872.74 is owed today, what was the original amount due? The note started out as a 120-month note.
THE SOLUTION This one has two parts.
  1. Find the interest rate on the note
  2. Find the original amount owed
First things first, make sure the calculator is using 12 Payments per Year. Step 1: Find the Rate N: 88 (There are 88 payments left) I/YR: (This is what I'm trying to find) PV: 32,872.74 (The borrower owes $32,872.74 today) PMT: -528.60 (The borrower pays $528.60 each month on the note) FV: 0 (The note amortizes fully)

The note's interest rate is 10%.

Step 2: Find the Original Balance N: 120 (There were originally 120 payments on this note) I/YR: 10 (From part 1) PV: (This is what I'm trying to find) PMT: -528.60 (The borrower pays $528.60 each month on the note) FV: 0 (The note amortizes fully)

The borrower originally owed $40,000.07. I'm going to assume that the actual amount at the beginning was an even 40 grand, and that the extra 7 cents is a result of a rounding error.

Note that we could have approached Step 2 differently: we could have made N 120 - 88 = 32, and put today's $32,872.74 into FV (from the perspective of Day One, today is 32 months in the future), making sure to make it a negative number. Solving for PV would have gotten us the same answer. Feel free to try it out if you don't believe me.

What do you think? Can you come up with situations in which knowing the original value of a thing helps you to better understand it today? If so, what's an example? Let us know in the comments!