A man deposited 8694 Egyptian pounds in a bank account with an interest rate of six percent per year. Determine how much money was in the account 10 years later, given that the interest was compounded annually. Give your answer correct to two decimal places.
So we can see from the question that what we’re looking at is compound interest because we’re told that the interest was compounded annually. So when we’re looking to find compound interest, we have a formula. And that formula is that the amount is equal to the principal amount, so that’s the amount we started with, multiplied by one plus 𝑟 all to the power of 𝑛, where 𝑟 is the interest rate as a decimal. And 𝑛 is the number of periods, so the number of periods of interest being added.
So what I’m now gonna do is extract the information from the question that’s gonna help us to solve this problem and plug it into the formula. So first of all, we’ve got 𝐴 which is the amount. And that’s the amount we’re looking for, so we don’t know that. Well then, we have 𝑃. Well, 𝑃 is gonna be 8694 Egyptian pounds. And that’s because 𝑃 is the principal amount or the amount that we started with. 𝑟 is going to be 0.06. And that’s because we’re told that the interest rate is six percent per year. And we know that six percent means six out of 100 or six divided by 100 or six hundredths is the same as 0.06.
Okay, so now, let’s see what 𝑛 is. Well, to work out 𝑛, we have to look at two bits of information. First of all, how often the interest is paid? Well, the interest is paid per year because it says six percent per year. Then we need to think, well in that case, over how many years are we looking to add interest? And the question again tells us because it says, we want to know how much money was in the account 10 years later. So, therefore, 𝑛 is equal to 10. And again, this is confirmed later in the questions cause it says that the interest was compounded annually.
So again, we know that it is gonna be every year. So we’ve got all the variables. Now, what we need to do is substitute them into our formula to solve to find the amount after 10 years. When we do that, we get 𝐴 is equal to 8694 multiplied by one plus 0.06 all to the power of 10 which is gonna give us 8694 multiplied by 1.06 to the power of 10. When we calculate this, we’re gonna get 15569.62987, et cetra.
Well, have we finished there? Well no, cause if we take a look at the question, it wants us to leave our answer to correct to two decimal places. So to round it to two decimal places, what we do is we go to the second decimal place which is two. And then, we look to the number to the right of this or the digit to the right of this. And this is gonna be our deciding number. And because this is five or above, we’re gonna round the two to a three. So we get a final answer that tells us that if the money was in the account for 10 years, then the value after that 10 years is going to be 15569.63 Egyptian pounds. And that’s to two decimal places.