Answer
The investment would double in value after about 11 and a half years.
Work Step by Step
We have an investment with a $6.25\%$ interest compounded annually.
That means every year, that investment would increase by $6.25\%$ of the amount available.
So, if we take the inital value of the investment to be $a_i$:
- After first year, it would increase by $6.25\%$ of $a_i$ -> now its value is $106.25\%a_i$ or $1.0625a_i$
- After second year, it would increase by $6.25\%$ of $1.0625a_i$ -> its value now is $1.0625\times1.0625a_i=(1.0625)^2a_i$.
Therefore, if we take $t$ to be the amount of time for the investment to double the money (which equals to $2a_i$), we have this equation:
$$(1.0625)^ta_i=2a_i$$
$$(1.0625)^t=2$$
Here, we use graphing calculator and find out that $$t\approx11.433\approx11.5(years)$$
So the investment would double in value after about 11 and a half years.
