# Future Value calculation and the Rule of 72

## Warning! Mathematics Alert!

## The Basics

Let’s say you have an asset worth $100 now, and you want to find out what it’s value will be in 5 years if it grows at a rate of 10% per annum and interest is compounded.

The equation is simple. The asset’s future value (FV) and present value (PV) are related as follows:

where i is the rate of interest and n is the number of periods. In our example:

Here the total growth over the 5 years FV/PV is 161.051/100 = 1.61051 . This gives us the total cumulative return r.

Or expressed in percentage terms:

(* equation A*).

In our example, (1.61051-1) x 100 = 61.051%.

If we rewrite the future value calculation to solve for i:

(* equation B*),

then substituting in for r and in percentage terms:

(* equation C*).

Note that equations marked A and C are quite symmetrical. The form of Equation B is termed the * compound annual growth rate* (CAGR).

If we wanted to solve for n, the formula becomes more involved:

Typically we can use the “Rule of 72” to derive a quick approximation for how long it will take to double an investment value.

## The Rule of 72

The Rule of 72 is a very simple way of illustrating the growth potential of compound interest. The rule says simply this:

where i is the interest rate in percentage, and n is the number of time periods needed to double the principal.

For example, say an investment fund grows at 12% average annual rate. According to the rule of 72, if money were invested in this fund, then it would double every 6 years (72/12 = 6).

However, the above Rule of 72 merely gives an approximation of the time needed to retain an investment before it doubles in value. The accurate calculation is as follows:

Alternatively, the Rule of 70, or 69.3 is used for more accuracy at lower interest rates.