How long will it take to double your money?

The value of your investments can go down as well as up. 

                                                 UK consumer financial advice

Recently you will have discovered that the value of your investments can plummet as well as go down. So, suppose you want to play safe and place cash in a straightforward savings account with a fixed, or slowly, changing rate of interest. 

How long will it take to double your money? 

Although nothing in this world is so certain as death and taxes (and the version of the latter that goes with the former), 

    let’s forget about them both and work out a handy rule of thumb for the time needed to double your money. Start out by putting an amount A in a savings account with an annual fractional rate of interest r (so 5% interest corresponds to r = 0.05), then it will have grown to A × (1+r) after one year, to A × (1+r)2 after two years, to A × (1+r)3 after three years and so on. 

After, say, n years your savings will have become an amount equal to A × (1+r)n. This will be equal to twice your original investment, that is 2A, when (1+r)n = 2. If we take natural logarithms of this formula, and note that ln(2) = 0.69 approximately, and ln(1+r) is approximately equal to r when r is much less than 1 (which it always is – typically r is about 0.05 to 0.06 at present in the UK), then the number of years needed for your investment to double is given by the simple formula n = 0.69/r. 

Let’s round 0.69 off to 0.7 and think of r as R per cent, so R = 100r, then we have the handy rule that 12 n = 70/R This shows, for example, that when the rate R is 7% we need about ten years to double our money, but if interest rates fall to 3.5% we will need twenty.

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