Question

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

Answer 1

$1718.22

Step-by-step 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) \\ (2500)/(1.455)=P \\ 1718.22=P \end{gathered}`

Therefore, the principal is $1718.22