42000 pounds is invested in an account offering simple interest at a rate of five percent per year. What is the value of the investment after four years?
Simple interest is a type of interest where the amount of interest paid by the bank account is the same every year. It’s calculated purely as a percentage of the amount of money that’s initially put into the bank account. In this case, it’s five percent of the initial investment. This differs from compound interest, where the amount of interest is recalculated every year. So you’re being paid interest on the interest you’ve already received. So each year, the amount of interest paid will be five percent of 42000.
Now there are a number of different ways that we could work this out. We can work out five percent of a number by dividing it by 20, because there are 20 lots of five in 100. 42000 divided by 20 is equal to 2100. Or we could first work out one percent by dividing 42000 by 100, which gives 420, and then multiplying this by five, which again gives 2100. Or we could convert five percent to a fraction.
Remember, “percent” literally means out of 100. So five percent is equivalent to the fraction five over 100. The word “of” in a calculation involving percentages means multiply. So five percent of 42000 is equal to five over 100 multiplied by 42000.
As expected, this will give the same answer of 2100. The final method would be to use decimals. Five percent or five over 100 is equivalent to the decimal 0.05. So we could evaluate 0.05 multiplied by 42000. Of course, this gives the same answer of 2100. So you can use any of these methods to calculate five percent of a number.
We know then that the amount of interest received each year is 2100 pounds. But the question asks us for the value of the investment after four years. The total amount of interest received in this period then will be four multiplied by 2100, because the question tells us that it’s a rate of five percent per year. The total amount of interest then is 8400 pounds.
Be very careful though, the question doesn’t just ask us for the total amount of interest paid. It asks us for the total value of the investment. To work this out, we need to take the initial investment of 42000 pounds and add it to the amount of interest received, which gives 50400 pounds. The value of the investment after four years then is 50400 pounds.