Assume the cost of a car is $21,000. 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 6.2%. Round the answer to the nearest hundredth.
A) 11.18 yr
B) 160.52 yr
C) 1.61 yr
D) 171.70 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. To double the cost, $A = 2P$, so $2 = e^{0.062t}$. Taking the natural logarithm of both sides gives $\ln(2) = 0.062t$, solving for $t$ gives $t = \frac{\ln(2)}{0.062} \approx 11.18$ years.

Assume the Cost of a Car Is $21,000