 1. Interest
2. Reverse percentages

Simple interest is calculated by multiplying the initial amount by the product of the interest and the number of time periods that have passed added to 1. This formula is given by X = A(1 + rt), where A is the initial amount, r is the interest rate and t is the number of time periods that have passed.

With compound interest, not only does the initial value receive interest, but also the additional interest for each time period. Compound interest is an example of exponential growth and decay that arise when there is an increase or decrease by the same factor over each time period. When a certain amount is equivalent to a certain percentage, divide both values by the value of the percentage to get the quantity equivalent to 1%. Multiplying both values by 100 will give the original value of the quantity. # 1

A shop has an ongoing sale of 40% off. Given that the reduction to a T-shirt is £12, calculate the full value of the T-shirt.

12 ÷ 40 = £0.30 is equivalent to 1%.
Multiplying by 100 gives £30 to be equivalent to 100% of the value.

£30 # 2

Given that 60% of a quantity is 75, calculate what the value equivalent to 38% is.

75 ÷ 60% = 1.25 is equivalent to 1%.
Multiplying by 38 gives that 47.5 is equivalent to 38%.

47.5 # 3

Given that 27% of a quantity is 54, calculate what the value equivalent to 72% is.

54 ÷ 27 = 2 is equivalent to 1%.
Multiplying by 72 gives that 144 is equivalent to 72%.

144 # 4

Beth has made an investment of £7000. Given that it accrues compound interest of 3% every year, calculate the value of her investment in 4 years.

Using the formula for compound interest, A = 7000(1 + 3% ÷ 100%)⁴ = £7878.56 (to 2 d. p.).

£7878.56 # 5

Anna has £200 in a bank account which accrues simple interest of 4% every year. Calculate the total amount she will have in 4 years.

Using the formula for simple interest, r = 4 ÷ 100 and t = 4.
total amount = 200(1 + 4 × 4% ÷ 100%) = £232

£232 End of page