Question

Comparing Two AlternativesSuppose that April has access to an investment that will pay 10% interest compounded continuously. Which is better: to be given \(1000 now so that she can take advantage of this investment opportunity or to be given \)1325 after 3 years?

Short answer

April is better to get$\$1000$to take advantage.

Step-by-step solution

Step 1. Given Information

Suppose that April has access to an investment that will pay 10% interest compounded

continuously.

The problem asks to find Which is better: to be given $1000 now so that she can take advantage of this investment opportunity or to be given $1325 after 3 years?

Step 2. Finding amount in April

$$\begin{gathered} P=\$1000 \\ r=10\%=0.01 \\ t=3years \end{gathered}$$

role="math" localid="1646326690319" $$\begin{gathered} A=P{e}^{rt} \\ A=1000\times e^{0.1\times 3} \\ A=\$1349.86 \end{gathered}$$

Step 3. Comparing the amount

Since$A=1349.86>\$1325$for April is better to get $1000 now.