How to Find Principal, Interest, or Rate
New lesson, let’s learn about simple interest and how to calculate terms that are missing. We’re given two problems and we’ll do one by—we’ll do them one by one. The first problem gives us—well, we need to find the interest. I = Interest and we need to find what it is, interest, right?
What are we given? We are given the Principal (P) = $250.00. We are given R which is the rate of interest, rate (r) = 4% and we are given (t) which is time and time is the amount of time that the money is earning interest, time (t) = 2 years, okay? So that’s what we’re given. Let’s take a little bit of space and try and figure out what is the interest that the principal amount of $250 we’ll earn, okay?
The formula that we want to use, we know that in case of simple interest, simple interest equals P x r x t and if (r) is in percent, we can convert (r) as percentage over a hundred. I’ll show you how to do that. But the interest is the multiplication of principal times the rate of interest in percent and time in years, right? So time needs to be in years as a unit, these needs to be in percent and principal can be in any currency as long as it’s money, okay?
So simple interest, I equals, well, what is P, principal is given to us as $250 times R which is given to us as 4% times T which is 2 years, okay? Since R is in percent, we can convert that to 4/100, right? 4% is the same as 4/100 x 2 which gives me 250 x 4 is a thousand, times 2 is $2000/100, almost there. Let’s divide both the top and the bottom by a hundred to get $20, okay? So the interest earned is $20 and the way we got that is by taking P, R and T and substituting it in the formula. Remember that R needs to be in percent, T needs to be in years and we convert R into 4/100, okay? Let’s do the second problem the same way.
We’re given the interest equals to 300, principal is a $1000 and we don’t know what R or the rate of interest is and we are given the time, okay? So let’s right this down. What are we given? Problem two, we are given interest equals $300,000, we are given principal equals $1000 rate, we are not given. We’re given time equals 5 years and rate, we have to determine. Okay, so let’s cool down and try and solve this one. So the formula again is I = P x r x, okay?
What are we given? Interest is $300, principal is $1000, (r) we don’t know and (t) is 5 years, okay? So based on this, what do we know? What we are given is—let’s multiply this. 300 is on the left end side, on the right end side is 1000 x 5. So 5000 x R, okay? Now let’s divide both sides by 5000 because what we want to do is leave R alone on one side, okay? So let’s divide both sides by 5000. So $300/$5000 = $5000 here, divide it by $5000 into R, right? All I did was divide the left end side and the right end side by $5000. So this will give me 300—I can remove the dollar sign actually, I don’t need it. 300/5000 equals R, right? Now, since 300/5000, if I divide the two, I will get this as 0.06 = r. Now rate always has to be in percent, right? This has to be n percent. So 0.06 = 6% because 0.06—I’m sorry, let me write this down. 0.06 = 6/100 because there are two digits to the right of the decimals point, we put one added by two zeros, right? 6/100 = 6%.
So the final rate that we were looking for is 6%. Quickly recapping, the key formula is I = P x r x t. R as in percent and T is in years. We’re given T, we’re given P and we’re given I. We solve for this to get R = 0.06 which is 6%.
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