This example continues the topic from pages 595-596 (The time value of money) in the book and further explains the time value of money.

The Time Value of Money: Examples

You can invest your money to generate a return (interest) of 10% per annum. This means that £1.10 for every £1 invested will be returned to you at the end of the year. Therefore, if someone were to offer you £100 today or £110 in a year’s time, you would be indifferent whether you received the £100 today or the larger sum in a year’s time. If you receive the £100 today, you can invest this £100 to generate £110 in a year’s time, so whichever option you choose you will still end up with £110.

However, if you are able to invest your money to generate a return of only 8%, the same offer will see you accepting the £110 in a year’s time as £100 invested today at an interest rate of 8% will produce only £108 in a year’s time.

Similarly, if you are able to invest your money to generate a return of 12% over the course of a year, you would accept the £100 today as you could turn this into £112 in a year’s time which is more than the £110 you have been offered.

Under the same principle, if you were offered £100 in a year’s time and interest rates are 10%, how much would you be prepared to accept today instead of the £100 12 months in the future? This requires a little more thought. £110 in a year’s time is equivalent to £100 today when interest rates are 10%. By dividing the £110 by 1.10 this gives us £100 today. £100 in a year’s time is thus worth £100 divided by 1.10 = £90.91. We can check this is correct by multiplying £90.91 by 1.10 and this gives us £100 in a year’s time. Thus, when interest rates are at 10%, £100 received in a year’s time has a present value today of £90.91, the sum you would need to invest at 10% interest to produce £100 in a year’s time.

What happens if you can invest your money for more than one year with interest earned on the first year’s interest in the second year (compound interest) as well as on the original money invested? If you were offered £100 today or £121 in two years’ time when interest rates are 10%, which amount of money would you accept? You could accept the £100 today and invest it to generate a return of 10% by the end of year 1: you would then have £110. By reinvesting the £110 for a further year to earn another 10% interest, you would have £121 (£110 x 1.10) so you would be indifferent between accepting £100 today and £121 in two years’ time.