Question

How much money invested at 5% compounded continuously for 3 years will result in $740?

Answer 1

Explanation

The question gives the following parameters

$\begin{gathered} \text{Rate = 5\%} \\ \text{Time = 3 years} \\ \text{Amount = \ 740} \end{gathered}$

Since the unknown principal is compounded continuously we can use the formula below to find the principal

$A=Pe^{rt}$

Next, we will insert into the above formula the values stated at the beginning of the solution.

$\begin{gathered} 740=Pe^{\frac{5}{100}\times3} \\ 740=Pe^{\frac{15}{100}} \\ Pe^{0.15}=740 \\ P=\frac{740}{e^{0.15}} \\ P=636.9239 \end{gathered}$

Answer: $636.9239