Choose the one alternative that best completes the statement or answers the question.
-Assume the cost of a car is $\$ 27,000$. With continuous compounding in effect, find the number of years it would take to double the cost of the car at an annual inflation rate of $9.1 \%$. Round the answer to the nearest hundredth.
A) $1.12 \mathrm { yr }$
B) $7.62 \mathrm { yr }$
C) $119.74 \mathrm { yr }$
D) $112.13 \mathrm { yr }$

Question

Quizplus · Accepted Answer

To find the number of years it takes for an investment to double with continuous compounding, use the formula $t = \frac{\ln(2)}{r}$, where $r$ is the annual interest rate (expressed as a decimal). For a $9.1\%$ rate, $r = 0.091$. Thus, $t = \frac{\ln(2)}{0.091} \approx 7.62$ years.

Choose the One Alternative That Best Completes the Statement or Answers