An investment is expected to pay 5% per year compounded continuously. If you want the value of the investment to be $900,000 after 25 years, how much should you invest initially? Round to the nearest dollar.
A)$64,464
B)$128,927
C)$257,854
D)$515,709
E)$429,203

Question

Quizplus · Accepted Answer

We can use the formula for continuous compounding:

$A = Pe^{rt}$

where A is the final amount, P is the initial investment, r is the annual interest rate (in decimal form), and t is the time period.

Plugging in the given values, we get:

$900,000 = Pe^{0.05 \cdot 25}$

Solving for P, we get:

$P = \dfrac{900,000}{e^{1.25}} \approx \$257,854$

Rounding to the nearest dollar, we get the answer of $\boxed{	extbf{(C)}\ 257,854}$.

An Investment Is Expected to Pay 5% Per Year Compounded