Warning! Mathematics Alert!
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:
In our example, (1.61051-1) x 100 = 61.051%.
If we rewrite the future value calculation to solve for i:
then substituting in for r and in percentage terms:
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.