Write the word or phrase that best completes each statement or answers the question.
-Assume the cost of a gallon of milk is $\$ 3.00$. With continuous compounding, find the time it would take the cost to be 5 times as much (to the nearest tenth of a year), at an annual inflation rate of $6 \%$.
A) $0.0 \mathrm { yr }$
B) $9.9 \mathrm { yr }$
C) $0.1 \mathrm { yr }$
D) $26.8 \mathrm { yr }$

Question

Quizplus · Accepted Answer

Using the formula for continuous compounding, $A = Pe^{rt}$, where $A$ is the future value, $P$ is the present value, $r$ is the rate, and $t$ is the time. Setting $A = 5P$, $r = 0.06$, and solving for $t$, we get $t = \frac{\ln(5)}{0.06} \approx 26.8$ years.

Write the Word or Phrase That Best Completes Each Statement $3.00\$ 3.00$3.00

Write the Word or Phrase That Best Completes Each Statement $\$ 3.00$