Question

What principal will amount to $2500 if invested at 5% interest compounded continuously for 7.5 years?

Answer 1

Answer:

$1718.22

Explanation:

For interest compounded continuously, we can use the following equation:

$A=Pe^{rt}$

Where A is the amount after t years, P is the principal and r is the interest rate.

So, replacing A = $2500, r = 5% = 0.05, and t = 7.5 years, we get:

$2500=Pe^{0.05(7.5)}$

Now, we need to solve for P, so

$\begin{gathered} 2500=Pe^{0.375} \\ 2500=P(1.455) \\ \frac{2500}{1.455}=P \\ 1718.22=P \end{gathered}$

Therefore, the principal is $1718.22