Question

The amount of money in an account can be determined by the formula A re where is the

initial investment, r is the annual interest rate, and tis the number of years the money was
invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest
compounded continuously?

Answer 1

`\$10272.17`

Explanation:

Since it is compounded continuously, we will use:

`A=A_0 \cdot e^(k t)`

`A_0` is the amount invested.

`k` is the rate.

`t` is the number of years you let the money sit.

`A` is the future amount after the
`t` years that has been accumulated.

(Note:

I'm going to write
`r=4%` as a decimal.
`r=(4)/(100)=0.04`.)

`A=5000 \cdot e^(0.04 \cdot 18)`

`A=5000 \cdot e^(0.72)`

`A=5000 \cdot 2.0544332` (approximated)

`A=10272.16605` (approximated)

To the nearest cent this is
`\$10272.17`.

Answer 2

Answer: $10272.17

Step-by-step explanation: Please see attachment for explanation