The purchasing power of a dollar is decreasing at the rate of 4.9% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.74? Round answers to the nearest hundredth.
A) 0.06 yr
B) 0.61 yr
C) 6.15 yr
D) 15.10 yr

Question

Quizplus · Accepted Answer

To find the time it takes for the purchasing power of $1.00 to decrease to $0.74 with a continuous annual decrease rate of 4.9%, we use the formula for continuous compounding: $A = Pe^{rt}$, where $A$ is the amount after time $t$, $P$ is the principal amount, $r$ is the rate of decrease, and $t$ is the time in years. Here, $A = 0.74$, $P = 1$, and $r = -0.049$ (since it's a decrease). Rearranging the formula to solve for $t$, we get $t = \frac{\ln(A/P)}{r}$. Plugging in the values, $t = \frac{\ln(0.74)}{-0.049}$, which approximately equals 6.15 years.

The Purchasing Power of a Dollar Is Decreasing at the Rate