The Simple Interest Formula

Welcome to a video on simple interest. The goal of the video is to use the simple interest formula to answer a variety of interest questions. Now, even though most banks use something called compounded interest, the simple interest formula is a nice way to develop an understanding of how interest affects the earnings on an investment or savings account, or how interest will affect how you pay back a loan. Interest represents a change in money. So if you have a savings account or investment account, interest will increase your balance based upon the interest rate paid by the bank, and if you have a loan, the interest will increase the amount you owe based upon the interest rate charged by the bank. The simple interest formula is I equals P times R times T, where I is the interest, P is the principal or starting amount, R is the rate expressed as a decimal, and T is time expressed in years. Let's go and take a look at some examples. If you invest $3,500 in a savings account that pays 4% simple interest, how much interest will you earn after three years, and what will the new balance be? So for this situation, we're trying to find I, or the interest, P, the principal or starting amount, would be $3,500, R is the rate of return, so R is 4%, but it must be expressed as a decimal, so this would be 0.04, and then T is time in years, so T is equal to three years. We have all the information we need to determine the amount of interest that's earned in this account. The interest will equal 3,500, the principal, times the rate of return as a decimal, 0.04, times the time in years, which is equal to three. So this product will give us our total interest over the three years. So we have 3,500 times 0.04 times three. So the interest earned will be $420. But they also ask us what the new balance of the account will be. So we take our starting amount, 3,500, and so this interest represents the increase in the balance, so we add $420, and so the ending balance will be $3,920. So again, we found the interest earned, and then we also found the new balance of the savings account after three years. Let's go and take a look at another example. You borrow $6,000 from a loan shark. If you will owe $7,200 in 18 months, what would be the simple interest rate? So now we're trying to find the interest rate, or R, so we should be able to determine I, P, and T. Let's see if we can do that. Remember I represents the amount of interest. So if you borrowed $6,000 and then you owe $7,200, the difference would represent the amount of interest. So the interest is going to be $7,200 minus $6,000. So our interest is equal to $1,200. P represents the principal or starting amount. The loan amount was $6,000. We're trying to solve for the interest rate. Now our time is 18 months, but remember that the time has to be expressed in years. Well since 18 months is 12 months plus 6 months, 18 months is equal to 1.5 years, or 1.5 years. So it is important that we do have to have our time in terms of years. So let's go ahead and set this up and see if we can solve for R. I, which is $1,200, must equal P, which is $6,000, times R, which we're solving for, times T, which is equal to 1.5 years. Let's go ahead and simplify the right side. $6,000 times 1.5 would be $9,000. So we'll have $1,200 is equal to $9,000R. Now we'll divide both sides by $9,000 to determine our interest rate. So we have $1,200 divided by $9,000. This is our interest rate expressed as a decimal. So to convert a decimal to a percentage, remember we can multiply by 100. So the interest rate is actually 13.3 repeating, or 13 and 1 3rd percent. Okay that's going to do it for simple interest. Thank you for watching.