Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 2 • Question 13

£2200 is invested for 5 years in an account offering simple interest at a rate of 3% per year. Work out the total interest.

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Video Transcript

2200 pounds is invested for five years in an account offering simple interest at a rate of three percent per year. Work out the total interest.

So this sum of money is being invested in a bank account and we’re told that this account offers simple interest at a rate of three percent per year. Simple interest means that the same amount of interest is paid every year. The rate is three percent per year, which means every year the interest received will be three percent of the initial investment. That’s three percent of 2200 pounds. We’ll look at how to calculate this in a moment.

This money is paid every year. And remember this 2200 pounds is invested for five years. So the total amount of interest paid in that period will be equal to five lots of three percent of 2200. That’s five times three percent of 2200.

Now, let’s think about how we work out this percentage. Percent literally means out of 100. So three percent means three out of 100 which we can write as the fraction three over 100. When we see the word of in a calculation involving percentages, we can replace it with multiply. So three percent of 2200 means three percent of three over 100 multiplied by 2200.

We can perform this calculation using fractions if we wish or we can convert to decimals. Let’s look at how we do with fractions first of all. We can cancel a factor of 100 from the 100 in the denominator and the 2200 in the numerator, giving three over one multiplied by 22. Three over one is just equal to three. So we have three multiplied by 22 which is equal to 66. This tells us that each year 66 pounds of interest is paid.

If we wanted to convert to a decimal instead, we recall that to divide by 100, we keep the decimal point fixed and move all of the digits two places to the right. So three over 100 is equal to 0.03. We can then calculate 0.03 multiplied by 2200 using a calculator and it gives 66 as before.

So each year, we’re going to be paid 66 pounds of interest. But we want the total interest. So we need to multiply this by five. That gives 330.

So we found that the total interest paid by a bank account offering simple interest at a rate of three percent per year if 2200 pounds is invested for five years is 330 pounds.

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