Video: Calculating Simple Interest Given Rate- Initial Investment- and Time

David deposited $500 in his new bank account at a simple interest rate of 5.68%. If he made no further deposits or withdrawals, how much money will be in his account after 2 1/2 years?

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Video Transcript

David deposited 500 dollars in his new bank account at a simple interest rate of 5.68 percent. If he made no further deposits or withdrawals, how much money will be in his account after two and a half years?

Let’s think about the money in his account after two and a half years. The money in his account will be his initial deposit plus the interest earned. We know this because he made no further deposits or withdrawals. His initial deposit is 500 dollars. The interest earned will be equal to the rate that he’s earning interest times the time that he earns the interest for times the initial deposit. We need to be careful here. The rate is 5.68 percent, and percent means out of 100. So we can write 5.68 percent as 5.68 over 100. Or we can write it as a decimal 0.0568. Considering the calculations we have to do, it’s more helpful to write it as a decimal.

Now, the time is given in years. We’re given the time David has kept his money in years as well. So we’ll take this mixed number, two and one-half, and we’ll write it as a decimal 2.5. And again, we’ll need to have his initial deposit of 500 dollars. The interest that David earned will be equal to 0.0568 times 2.5 times 500. When we do this multiplication, we get 71. That means that David earned 71 dollars in interest. And it means that after two and a half years, his account will have 571 dollars.

Let’s consider one other way to solve this problem. We could have taken the 500 dollars of the original investment, multiplied it by the rate written as a decimal 0.0568. When we type that into our calculator, we get 28.4, which we know means 28 dollars 40 cents. And that means David earned 28 dollars 40 cents in the first year. He made no deposits or withdrawals and would, therefore, earn in the same amount in year two. After that, though, we have a half a year, and that means he would earn half of 28 dollars and 40 cents, which is 14 dollars 20 cents. If we add up your one, two, and half of your three, we get 71 dollars. And to that we add his starting amount. And so again, we see that after two and a half years, David will have 571 dollars in this account.

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