If you receive $15,000 today and can invest it at a 8.00% annual rate compounded continuously,what will be your ending value after 20 years?
A) $63,894.12
B) $56,464.57
C) $74,295.49
D) $92,869.36
E) $80,982.08

Question

Quizplus · Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. Given $P = $15,000$, $r = 8\% = 0.08$, and $t = 20$ years, we calculate $A = 15000 \cdot e^{0.08 \cdot 20} = 15000 \cdot e^{1.6}$. This calculation gives us $A ≈ $74,295.49$, which matches option C.

If You Receive $15,000 Today and Can Invest It at a 8.00