Question

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

Answer 1

Step-by-step 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^{(5)/(100)*3} \\ 740=Pe^{(15)/(100)} \\ Pe^(0.15)=740 \\ P=(740)/(e^(0.15)) \\ P=636.9239 \end{gathered}`

Answer: $636.9239