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## Pre-paying for a discount

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 Several years ago, I moved from a medium-sized house with a garage to a small condo with no garage. As you might imagine, some of the 'treasures' I'd accumulated and stuffed into my house and garage just don't fit into the much-smaller condo. So I did what so many of us do and rented a storage unit to keep the items I just couldn't bear to part with (this was after seven van-loads of donations to the local Goodwill). The storage center my extra stuff is currently housed in charges \$176 per month for a 10'x10' unit like mine (now I know what business I should really be in). However, if you pay for 6 months in advance, they'll give you the sixth month for half off. So my question is "if I pre-pay for six months, what's the return on my up-front money?"
THE SOLUTION It's useful to re-state the problem to put it in terms that make it easier to plug into the calculator. First off, I need to figure out how much money I have to pay up-front. Since they're giving me Month 6 at half off, that means that I have to pay for 5 ½ months today to rent the unit for the next six months. Since once month costs \$176, I have to pay \$176 x 5.5 = \$968 today. So the restatement of the problem goes like this: I'm going to pay \$968 now to save myself a \$176 monthly payment for the next six months. First things first, make sure the calculator is using 12 Payments per Year. N: 6 I/YR: (this is what I'm trying to find) PV: -968 (the amount I need to pay today...) PMT: 176 (... to save this much each month) FV: 0

The answer to the question is 30.53%. So if I pre-pay for six months, I'm actually making over 30% on my money.

Making 30% on your money is something that, if you do it consistently and with enough money, can leave you pretty wealthy after a relatively short period of time. However, contrary to sales pitches in the vein of 'The more you buy, the more you save!', it usually doesn't make sense to spend money just to get a discount on the price. If you can avoid the price (discounted or not), you're generally better off. If I were to move into a bigger place or have a change of heart and decide to liquidate everything in the storage unit, I'd save myself \$176 per month without the \$968 payment every six months. And that would leave me nearly \$2,000 per year richer than I am now.

What do you think? Do you have any pre-payment opportunities on your regular monthly payments, and if so, what's the return on those up-front payments? Let us know in the comments below!