Ever wonder why you pay interest on money you borrow, or collect it on money you lend? For many, it’s one of those questions that seems obvious yet hard to nail down exactly. At the heart of the matter is the time value of money. Put simply, it’s better to have a dollar in your pocket today than to be promised a dollar in a week from today. Why? For one reason, if the dollar is in your pocket, there is no risk that you won’t get it, because you already have it. A lot of things can happen between now and next week that could put that future dollar payment at risk. It’s worth something to be sure that you have the dollar today compared to next week, and that’s one facet of money’s time value.
Another reason you’d rather have your money today is that you can spend it today if necessary. If you need that dollar to buy a loaf of bread, you don’t want to go hungry for a week waiting to receive your dollar.
But you’re a reasonable person. You tell your friend that you’ll accept the one-week delay if you’re paid something extra to compensate for the wait. That extra something is interest, and it compensates you for waiting to receive your money. After some haggling, you agree to take $1.02 in a week or $1.00 today. While that doesn’t seem like much, remember that there are 52 weeks in the year, so if you waited a year to accept the dollar, you could demand $0.02 x 52, or $1.04 in interest. In one year, you’d receive the original dollar plus $1.04 in interest, giving you a final payment of $2.04. That’s a simple annual interest rate of 104 percent.
If you are mathematically inclined, you can use the following formula:
A = P(1 + rt)
Where A is the total amount, P is the principal ($1), r is the interest rate (104%) and t is time (one year). So,
A = $1.00 (1+ 104* 1)= $2.04.
However, you insist on a little tweak to the deal. You want the interest to compound monthly. Compounding means you add the interest you’ve earned so far to the original principal, so that you begin earning interest on interest. For monthly compounding, you add in your interest every month. It turns out that you will receive $2.71, which works out to and extra $1.67. You like compounding so much, you demand it be performed daily, and voila, the amount mushrooms to $2.83, an extra windfall of $1.79 compared to simple interest.
OK, we know that this is pretty rudimentary for most of our readers. But it’s necessary background when you start considering net present value and internal rate of return, two very important numbers when contemplating the financing of a fix-and-flip project. And that’s exactly what we’ll do in our next blog article.