# How do you determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25% compounded annually?

Sep 4, 2016

Time reqd. $\text{appr. "11.45" yrs.}$

#### Explanation:

Let the Principal $P$ be doubled in $n$ years at the given rate.

We know that $A = P {\left(1 + \frac{r}{100}\right)}^{n}$

Here, A=2P, P=P, r=6.25%, n=?

$\therefore 2 P = P {\left(1 + \frac{6.25}{100}\right)}^{n}$

$\therefore 2 = {\left(\frac{17}{16}\right)}^{n}$

$\therefore {\log}_{10} 2 = n \left({\log}_{10} 17 - {\log}_{10} 16\right)$

$\therefore 0.3010 = n \left(1.2304 - 1.2041\right) = n \left(0.0263\right)$

#:. n=0.3010/0.0263~~11.45

Hence, time reqd. for the purpose is $\text{appr. "11.45" yrs.}$