Assume the cost of a gallon of milk is $2.60. 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) 23.1 years
B) 35.9 years
C) 0.1 year
D) 8.5 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 $t$ is the time in years. To find the time it takes for the cost to quadruple, set $A = 4P$ (since 4 times as much as the initial amount), $P = \$2.60$ (which will cancel out), and $r = 0.06$ (6% annual inflation rate). Solve for $t$: $4 = e^{0.06t}$. Taking the natural logarithm of both sides gives $ln(4) = 0.06t$, so $t = ln(4)/0.06 \approx 23.1$ years.

Assume the Cost of a Gallon of Milk Is $2