How long will it take $1,500 to double itself if it is invested at 5% interest compounded semiannually? Please round the answer to the nearest tenth.

Question

Quizplus · Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. To double the money, $A = 2P$, so $2P = P(1 + \frac{r}{n})^{nt}$. Plugging in the values given: $2 = (1 + \frac{0.05}{2})^{2t}$. Solving for $t$ gives approximately 14.0 years.

How Long Will It Take $1,500 to Double Itself If