Video: Forming and Evaluating Exponential Functions Involving Exponential Growth and Compound Interest

A man invested 200,000 LE in a project. Each year his investment grows by 9%. Determine the value of his investment after 7 years, giving your answer correct to two decimal places.

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Video Transcript

A man invests 200000 Egyptian pounds in a project. Each year his investment grows by nine percent. Determine the value of his investment after seven years, giving your answer correct to two decimal places.

So, in this question, we’ve got three key bits of information. We have the amount that the man is investing. We have the amount it grows by. And we also have the number of years that he’s investing it. And what we’re gonna use here is something called compound interest. And we have a formula to help us work out compound interest.

And this formula is that 𝐴, so the amount of the investment, is equal to 𝑃, and 𝑃 is our initial investment, multiplied by one plus 𝑟, where 𝑟 is the interest rate as a decimal. And this is all to the power of 𝑛, and 𝑛 is the number of periods over which the investment has been invested. So, in our case, it’s gonna be the number of years.

So, in this question, I said it was compound interest. That’s because we’re told that each year the investment grows by nine percent. However, the difference between compound and simple interest is that in compound interest you get interest on the interest that you gained the year before. If it was something where it was simple interest, then all we do is work out the interest for one year, and then multiply this by the number of years there are.

Okay, so, now we have our formula. Let’s use it to find out the answer to the question. So, first of all, let’s write down the information that we’ve been given. So, we’ve got 𝑃, our initial investment, is 200000 Egyptian pounds. And then we’ve got 𝑟 is equal to 0.09. And that’s because it’s our interest rate as a decimal. And our interest rate is nine percent. And we get that because nine percent means nine out of 100, or nine over 100, or nine divided by 100, is 0.09. And that’s because if we’re gonna divide by 100, we’re gonna move the nine two place values to the right. So, as we’ve said we get 0.09.

And then, 𝑛 is seven. And that’s because that’s the number of time periods. But it’s worth noting that even the question says that it’s after seven years we want to work out the investment, we definitely know that 𝑛 is seven. Because we’re told that each year the investment grows by nine percent. If it talked about each month or each week or each quarter the investment growing by certain percentage, then 𝑛 would be a different value because we’d have to look at how many time periods the interest had been over.

So then, to work out the answer to the question, so we work out the value of the investment after seven years, we substitute our values into our formula. And when we do that, we get 200000 multiplied by one plus 0.09 all to the power of seven. Which if we simplify, gives us 200000 multiplied by 1.09 raised to the power of seven. Which when calculated gives us an answer of 365607.8242. Well, we haven’t finished there. And that’s because the question wants us to give our answer correct to two decimal places.

So, to do that, the second decimal place is two because it goes 0.82. So, what we do is we look to the digit to the right of the two. This is our deciding number. And because this is below five, because it’s a four, then that means we’re gonna round down and the two will remain the same. So therefore, we can say that if a man invested 200000 Egyptian pounds in a project and each year his investment grew by nine percent, then the value of his investment after seven years correct to two decimal places would be 365607.82 Egyptian pounds.

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