Choose the one alternative that best completes the statement or answers the question.
-How long will it take for $\$ 6100$ to grow to $\$ 26,700$ at an interest rate of $4.6 \%$ if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A) $3.21 \mathrm { yr }$
B) $1.01 \mathrm { yr }$
C) $32.10 \mathrm { yr }$
D) $3209.51 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To solve this, we use the formula for continuous compounding interest: $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (\$6100), $r$ is the annual interest rate (4.6%, or 0.046 as a decimal), and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Plugging in the values, $t = \frac{\ln(26700/6100)}{0.046}$, which calculates to approximately 32.10 years.

Choose the One Alternative That Best Completes the Statement or Answers