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## Comparing Two Discounts

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**THE SCENARIO**
A while back, I covered a discount offered by a storage place in which I rent a unit. Some time has passed, and they now have *two* different discounts that I can choose between. They're as follows:
**The question:** If my rent is $200 per month, which of the options gives me a better return on my money?

**THE SOLUTION**
This one is pretty simple, and has three parts, none of which is overly complicated.
**Part 1: Evaluating paying for 5½ months but getting 6**
First off, I have to figure out my prepay rent. $200 x 5.5 = $1,100
N: 6 (I get 6 months worth of rent by prepaying)
I/YR: (This is what I'm trying to find)
PV: -1,100 (When I prepay, I fork over $1,100)
PMT: 200 (I'm saving myself $200 per month by prepaying)
FV: 0 (At the end, I owe rent again)
**Part 2: Evaluating paying for 11 months but getting 12**
First off, I have to figure out my prepay rent. $200 x 11 = $2,200
N: 12 (I get 12 months of rent by prepaying)
I/YR: (This is what I'm trying to find)
PV: -2,200 (I have to give them $2,200 up front to pay my rent for a year)
PMT: 200 (I'm saving myself $200 per month by prepaying)
FV: 0 (At the end, I owe rent again)
**Part 3: Comparing the two**
If I prepay for 6 months, my yield is 30.53, but if I prepay for 12 months, my yield drops to 16.38.
And that's generally the way this works - doubling the time cuts the yield (roughly) in half. Halving the time (roughly) doubles the yield.
But why?
The short answer is: Time. In the 6 month scenario, I don't have to wait nearly as long to get my money back, to 'make a profit', or to 'be in the black' on the deal. I get half a month's rent after 5 ½ months, rather than waiting twice as long to see my profit. If that's a hard concept to wrap your mind around (it was for me, at first), try playing around with your calculator, running different scenarios, and you'll see that it ends up being true - get your profit sooner, and your yield goes up. Wait for your profit, and your yield goes down. That's because the way we represent yield is *Per Year* - Time is baked into the equation.

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- Pre-pay for 6 months, and get the last month half off (i.e. pay for 5 ½ months, but get 6)
- Pre-pay for 12 months, and get the last month for free (i.e. pay for 11 months, but get 12)

- Determine the yield for the 6-month discount
- Determine the yield for the 12-month discount
- Compare the yields

My yield on 6-month prepayment is **30.53%**.

My yield on 12-month prepayment is **16.38%**.

What do you think? Did you expect this outcome? Are you surprised by it? Do you even believe it? Have you run across similar prepayment discount opportunities in your life? Let us know in the comments!