Question

How would you use A = Pe^rt to solve home much will be in your account in 5 years if you deposit $2000 in a continuously compounding savings account and pays an annual interest of 4%?

Answer 1

We want to use the formula

`A=Pe^(rt)`

to solve the question, here

`\begin{gathered} A=\text{ amount after 5 years = ?} \\ P=\text{ principal/money deposited = 2000 dollars } \\ t=\text{ time in years = 5 years} \\ r=\text{ annual interest rate = 4 percent = }(4)/(100)=0.04 \end{gathered}`

Substituting the values, we have

`\begin{gathered} A=Pe^(rt) \\ A=2000* e^(0.04*5) \\ A=2000* e^{(1)/(5)} \\ A=2000*1.22140 \\ A=2442.8055 \end{gathered}`

Hence the answer is $2442.81 to the nearest cent