Solve the problem.
-Assume the cost of a gallon of milk is $2.50. With continuous compounding, find the time it would take the cost to be 2 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.
A) 11.6 years
B) 0.1 years
C) 0.2 years
D) 4.2 years

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal amount, $r$ is the rate, and $e$ is the base of the natural logarithm. Here, we want the amount $A$ to be twice the principal $P$, so $2P = Pe^{0.06t}$. Dividing both sides by $P$ and taking the natural logarithm of both sides gives $\ln(2) = 0.06t$. Solving for $t$ gives $t = \frac{\ln(2)}{0.06} \approx 11.6$ years.

Solve the Problem. -Assume the Cost of a Gallon of Milk Is $2.50