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How discounted is that note really? Part 1

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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!

This post was inspired by a customer who asked us for some help solving a problem.  We asked him if it was okay with him if we did a Money Blog post about a situation like his, and he said that would be fine.  So here goes!


I came across a note for sale.  The terms of the note are as follows:

Original balance: $6,000

Unpaid balance as of June 2: $4,560

Term: 5 years

Interest Rate: 0

Payments: $100 per month

If I buy it, make the purchase on June 2, and the first payment I'll receive will be the July payment.

Every February, the borrower pays off $1,000 in order to accelerate the note paydown.


If the borrower continues to pay on his normal schedule (including the extra $1,000 every February), how much longer will he continue to owe the note's owner anything?


I'll start receiving money in July.  That means that I'll receive $100 for each of July through January (6 payments for a total of $600), then $1100 in Febuary, then $100 for each of March through January (11 payments for a total of $1,100), and so on.

So as of next January, the borrower will owe me $4,560 - $700 ($100 per month for 7 months) = $3,860.

After February, he'll owe me $3,860 - $1,100 = $2,760.

As of the following January, he'll owe $2,760 - $1,100 ($100 per month for 11 months) = $1,660.

After that Febuary, he'll owe $1,660 - $1,100 = $560.

He'll be all paid off six months after that.

Adding it up, I get 7 months + 1 month + 11 months + 1 month + 6 months = 26 months.

I'm decent at using a spreadsheet, so here's how I set up the problem and solved it in Excel: