What is a compound rate?

Answer 1

With a compound interest rate (as distinct from a simple interest rate), you take a certain percentage, add it to your total, and then calculate the level of interest for the next period from your new value. For example:

If you have £1,000 at a compound interest rate of 10%, increasing monthly:

After the first month, your money has increased to £1,000 + 10% = 1000 x 1.10 = £1,100.
After the second month, your money has increased to £1,100 + 10% = 1100 x 1.10 = £1,210
After the third month, your money has increased to £1,210 + 10% = 1210 x 1.10 = £1,331.

Rather than continuously multiplying by the same amount, however, we can use the power function. So, after two months at a compound interest rate of 10%:

£1,000 is equal to:

£1,000 x 1.105 = £1,610.51

A general formula, where X is the present value, and y is the future value:

x * (1 + r)n = y

Where r is the interest rate, and n is the number of periods. The addition of 1 indicates that it is a percentage increase we are looking for, and not merely a percentage.