Assume the cost of a gallon of milk is $3.40. With continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.
A) 0.1 yr
B) 8.5 yr
C) 0.0 yr
D) 23.1 yr

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, $A = 4 \times 3.40 = 13.60$, $P = 3.40$, and $r = 0.06$. Solving for $t$, we get $t = \frac{\ln(A/P)}{r} = \frac{\ln(4)}{0.06} \approx 23.1$ years.

Assume the Cost of a Gallon of Milk Is $3