An investment of $500 is made in a trust fund at an annual interest rate of 5%, compounded monthly. How long will it take for the investment to double? Give your answer to two decimal places.
A) $13.89$ years
B) $166.70$ years
C) $1.06$ years
D) $13.86$ years
E) $20.00$ years

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 investment, $A = 2P$, so we have $2P = P(1 + \frac{r}{n})^{nt}$. Plugging in the values $P = 500$, $r = 0.05$, and $n = 12$ (since the interest is compounded monthly), we solve for $t$. Rearranging the equation gives us $2 = (1 + \frac{0.05}{12})^{12t}$. Solving for $t$ gives approximately $13.86$ to $13.89$ years, with the correct answer being rounded to two decimal places as $13.89$ years.

An Investment of $500 Is Made in a Trust Fund 13.8913.8913.89

An Investment of $500 Is Made in a Trust Fund $13.89$