Given an amount is £P over a period of time, n years at r% interest. How can I calculate the year when £P will be double?
The well-known compound interest formula, $$P\left(1+\frac{r}{100}\right)^n$$
The time period when the money will be double
algebra-precalculus
Best Answer
The amount by which $P$ is multiplied is $\left(1+\frac{r}{100}\right)^n$. Hence the money doubles when this factor is equal to $2$, that is, when
$$\left(1+\frac{r}{100}\right)^n = 2.$$
Solving for $n$ (make sure you understand how to do this using logarithms!), this gives $$\boxed{n = \frac{\log 2}{\log\left(1+\frac{r}{100}\right)}}.$$
The boxed formula tells you how many years ($n$) it takes for the money to double. Given a value of $r$, you can use your calculator to obtain the value of $n$.