Solve the problem.
-$5832 is deposited into a savings account at 9% interest, compounded monthly. To the nearest year, how long will it take for the account balance to reach $1,000,000?

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. Here, we are given $P = 5832$, $r = 0.09$ (since 9% as a decimal is 0.09), $n = 12$ (since the interest is compounded monthly), and $A = 1,000,000$. We need to solve for $t$.Rearranging the formula to solve for $t$, we get:$$t = \frac{\log(A/P)}{n \cdot \log(1 + r/n)}$$Plugging in the values:$$t = \frac{\log(1,000,000/5832)}{12 \cdot \log(1 + 0.09/12)}$$$$t \approx 56.7$$Rounding to the nearest year gives us 57 years.

Solve the Problem. -$5832 Is Deposited into a Savings Account at 9% Interest