How to Calculate the Rate When 3 Values Are Known
Question
Supposed you have \$1600 and you want to make \$400 in 2 years, what should the interest rate be?
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How to Calculate the Rate When 3 Values Are Known

Hi, my name is Bassem Saad. I'm an associate math instructor and a math Ph.D. candidate, and I'm here today for About.com to show you how to calculate the rate when three values are known – by the rate we mean the interest rate.
Learn the Simple Interest Rate Formula

Although there are lots of interest formulas, we're going to be looking at the Simple Interest Formula. That is, this function with r as the annual interest rate, t as the number of years, p as the principle investment, and I sub s as the money earned from the interest rate. This could be the money earned or the money owned depending on whether you're investing money or borrowing money. So if we solve for r, we get this equation: that is the rate equals money that you earn, divided by the principle, times the time.
Practice Problems for Simple Interest Rate

So if we ask the question: Suppose you have \$1,600 and you want to make \$400 in two years, what would the rate need to be – that's r. So we plug it into our equation. The money earned is \$400, divided by the number of years, times the money invested. This gives us an interest rate of 12.5 percent.

Let's take a look at another example: Suppose you plan to borrow \$1,000 and pay it all back in six months, but you don't want the interest fees to exceed \$50. What would be the largest acceptable interest rate? So we can plug our numbers into our formula. The interest fees is I-s, so we plug the \$50 into I-s. The principle is \$1,000, so we plug the principle into P. And the number of years – well, it's actually six months, but we want it in terms of years. So there are 12 months in a year, so we divide six by 12 to give us point five. So we plug point five into t. After putting all these numbers into our formula we have that the rate equals point one, or ten percent.

So that's how to find the interest rate when three values are known. Thanks for watching, and to learn more visit us on the web at About.com.