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:: How to Calculate Future and Present Values ::

1. Calculating Future Value

If you invest £1,000 today for 3 years at annual interest rate of 10%, at the end of the third year, this present value (PV) £1,000 will increase to a value of £1,331, assuming all interests received are reinvested:

Therefore

where r is the annual interest rate, t is the number of years. If, however, the money is compounded on a semi-annual basis, the future value is then:

where n is compounding frequency per year, e.g. n = 2 if interest is calculated semi-annually.

In the previous example, the future value of £1,000 compounded semi-annually at 10% for 3 years will be:

In France and Germany, most corporations pay interest on their bonds annually. In U.S. and Britain, most pay interest semi-annually.

Some financial instruments also pay at continuously compounded rate, i.e. payments are assumed to spread evenly and continuously throughout the year, where n approach infinity:

Here e is the base for natural logarithms and has the value 2.718281828.

2. Calculating Present Value:

The formula for calculating present value is simply the reciprocal of the future value formula:

Note that for loans where interests are paid annually, n = 1.

Written by Henry Tang

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