How long will it take $800 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.
A) 14.0 years
B) 17.0 years
C) 14.5 years
D) 13.0 years
E) 15.0 years

Question

Quizplus · Accepted Answer

To find the time it takes for an investment to double with compound interest, you can use the formula $t = \frac{\log(2)}{\log(1 + r/n)} \times \frac{1}{k}$, where $r$ is the annual interest rate (as a decimal), $n$ is the number of times the interest is compounded per year, and $k$ is the number of years. For this problem, $r = 0.05$, $n = 2$, and we want to solve for $k$. Plugging these values into the formula gives $t = \frac{\log(2)}{\log(1 + 0.05/2)} \times \frac{1}{2}$, which approximately equals 14.0 years.

How Long Will It Take $800 to Double Itself If