Answer
The time required for an amount of money to double in value is given by $t = \frac{1}{r}$
Work Step by Step
This is the formula we use when we make calculations with simple interest:
$A = P~(1+rt)$
$A$ is the future value
$P$ is the present value
$r$ is the interest rate
$t$ is the number of years
Let's suppose that the future value is $2P$. We can find the time $t$ that is required to reach this future value.
$A = P~(1+rt)$
$2P = P~(1+rt)$
$2 = 1+rt$
$rt = 1$
$t = \frac{1}{r}$
The time required for an amount of money to double in value is given by $t = \frac{1}{r}$
