A man deposited 1,078 Egyptian pounds in a bank account with an interest rate of 7 percent per year. Determine how much money was in the account five years later, given that the interest was compounded monthly. Give your answer to the nearest pound.
In this question, we will need to calculate the compound interest. There are two formulas that we can use to calculate compound interest. In the first formula, we calculate the compound interest when the interest is simply compounded annually. But here, we’re told that the interest is compounded monthly. And so we need to use this formula, which takes into account the interest compounded 𝑛 times a year. 𝑉 is equal to 𝑃 times one plus 𝑟 over 𝑛 to the power of an 𝑛𝑦. 𝑉 represents the value of the return of the investment. 𝑃 is the principal or starting value. 𝑟 is the annual interest rate. 𝑛 is the number of times per year the interest is compounded. And 𝑦 is the number of years.
So let’s make a note of these values from the question. 𝑉, the value of the return, is what we wish to calculate. The principle is what the man begins with. That’s 1,078 Egyptian pounds. The annual interest rate is 7 percent, which we can write as a decimal as 0.07. We’re given that the man invests the money for five years. So that’s the value for 𝑦. Finally, we’re told that the interest is compounded monthly. And we know that there are 12 months in a year, so the number of times per year the interest is compounded means that 𝑛 is equal to 12.
We then substitute these values into the compound interest formula. And that gives us 𝑉 is equal to 1,078 times one plus 0.07 over 12 to the power of 12 times five. And of course, 12 times five simplifies to 60. And now, we can take this calculation and put it into a calculator. This gives us 1,528.2000 and so on. And we need to round this to the nearest pound. This will give us an answer of 1,528 Egyptian pounds.
It’s always good just to check our answer. And here, a good check would be that the value of the return is indeed larger than the starting value and a sensible amount larger. Also, a common mistake is to forget to change the interest rate into a decimal or a value over 100. If we had forgotten to change it and we’d used incorrectly a fraction of seven over 12, we would have got a return investment in terms of billions of Egyptian pounds. Here, we can give the answer then that 1,528 Egyptian pounds is the money in the account after five years.