Question

4500 is invested in a account that earns 3.8% yearly interest rate commpoundly continuously. How much will account have after 5 yrs.

Answer 1

`\text{ After 5 years the account will have \$5,442}`

Explanation:

Continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest. It is represented as:

`\begin{gathered} A=Pe^(rt) \\ \text{where,} \\ P=\text{ principal} \\ r=\text{ rate} \\ t=\text{ time in years} \\ e=\text{ approx. }2.7183 \end{gathered}`

Then, for $4,500 invested at a rate of 3.8%, after 5 years you will have:

`\begin{gathered} A=4500\cdot(2.7183)^(0.038\cdot5) \\ A=\text{ \$5,441.6} \\ \text{ Rounding to the nearest dollar:} \\ A=\text{ \$5,442} \end{gathered}`