4.6e Translate Percents And Applications - Simple interest

4.6e: Translate percents and applications - simple interest Interest is payment from an investment. It can also be additional amount that you must payback in the form of interest on a loan. Simple interest equation is that I = PRT. Each one of these letters represent something we will find in the equations. "I" is the interest. "P" is the principle. Principle is essentially a fancier word or the idea that it is the amount that you invested or the amount that you borrowed. "R" is the rate. The rate, remember, is a percent. And finally, "T" is the time. The key here that time must be in years. It is very important that the time is in years. If it is not written in years, you will not be calculating the appropriate values. If your number is in months, you put the months over 12 because there are 12 months in a year. If your time is in weeks you put your weeks over 52 as there are 52 weeks in a year. If you time is in days, you will therefore put your time over 365 because there are 365 days in a year. In example 1, it asks, a bank account pays 2.1% simple interest on a certain account. If you invest $3,500 for four years, how much will you earn in interest? You need to find each of the values and determine which portion of the formula they go into. It says that there is 2.1% interest so this is our percent or the "R." Next, it tells us how much we invested. If we invested $3,500, this means this is our principal or the price we invested. Next, it says that we invested for four years. This means our "T" is 4. We also see that it is in years, so we will not be needing to divide it by anything. Finally, it asks us how much will you earn in interest, so it wants to know the interest. We start by writing out the equation that I = PRT. "I" is what we are looking for, so we do not put any value there. The "P" is $3,500. The "R" is 2.1, remember that this must be written as 2.1 over100 since it is a percent. Next, we have the time or years, it is 4. All of these are multiplied together because, remember, if there is no symbol between two variables or two terms we know that they are being multiplied. We start by doing the fraction first and determining that 2.1 is actually .021. All other portions of the equation are unchanged. We can now type this in our calculator and find that the interest we will earn is $294.00. In example 2 asks, a bank gives a loan with 4.5% simple interest for 9 months on a $12,000 loan. How much is owed back to the bank at the end of the loan? We need to identify each of the pieces. First, we see that the simple interest is listed as 4.5. This means this is our rate or percent. Next, we see that it is loaned for 9 months. 9 months is our time. Remember that since it is months. We must divide our time by 12. Finally, we have the $12,000 loan. This tells us how much the principle or original amount was. It then asks how much is owed back to the bank at the end of the loan. As you noticed here, it did not ask how much interest you will have to payback but just how much is owed back to the end of the load which means we will have to an additional calculation. We will start by finding the "I." "I" is our interest. We know that the interest equals PRT or the principle times the rate times the time. Our principle is $12,000. Next, our rate is 4.5 which, remember, is 4.5 over 100. Finally, we have our time but, remember, it was in months, so we need to do 9 over 12. We now figure out what the two fractions are as decimal forms so we get .45 for the rate and for the other fraction it is easier if we put it as the decimal and we will get .75. We may now enter this into our calculator to find the interest. We find that the interest will be $405.00. If we look back at what the question asked, it did not ask the amount of interest but asked how much we will be paying back at the end of the loan, which means that we will have to pay the original amount we borrowed of $12,000 plus the interest which was $405.00, so we would be adding these together to find that we would need to pay $12,405. This is the total amount to be paid back. Remember that when you are finding interest that you must have your time in years. If it is not years, you must do the appropriate number below it to turn it into either 12 for months, 52 for weeks, or 365 for days. Also remember to clearly read the problems to assess whether they are asking for the interest or specific value other than that or if they are asking for a total amount to be paid back or total amount you would get in return.