# If $50 is invested at 6 percent interest. How long will it take to double? ##### 1 Answer Nov 11, 2016 16 years and 8 months with simple interest earned 11 years and 11 months with compound interest earned #### Explanation: The time will differ between an investment with compound interest and with simple interest. It will happen sooner with Compound interest. Simple interest: In order to double in value, the interest must be $50

$S I = \frac{P R T}{100} \text{ } \rightarrow \frac{50 \times 6 \times T}{100} = 50$

$T = \frac{100 \times 50}{50 \times 6}$

$T = \frac{100}{6} = 16.6666 = 16 \frac{2}{3}$ years

16 years and 8 months to double with simple interest

Compound interest

In order to double, the Amount must be $100 $A = P {\left(1 + \frac{R}{100}\right)}^{n}$$50 {\left(1 + 0.06\right)}^{n} = 100$${\left(1.06\right)}^{n} = \frac{100}{50} = 2$$n \log \left(1.06\right) = \log 2$$n = \log \frac{2}{\log} 1.06$$n = 11.89$years $n \approx 11\$ years and 11 months