Question

Anjali invests a sum of money in a retirement account with a fixed annual interest rate of 6.79% compounded continuously. After 20 years, the balance reaches $14,037.16. What was the amount of the initial investment?

Answer 1

The initial investment was of $3,610.

Explanation:

The continuous interest formula is:

`P(t) = P(0)e^(rt)`

In which P(t) is the amount of money after t years, P(0) is the initial amount invested and r is the fixed interest rate.

6.79% compounded continuously.

This means that
`r = 0.0679`

After 20 years, the balance reaches $14,037.16.

This means that
`t = 20, P(t) = 14,037.16`

What was the amount of the initial investment?

This is P(0).

`P(t) = P(0)e^(rt)`

`14037.16 = P(0)e^(0.0679*20)`

`P(0) = (14037.16)/(e^(0.0679*20))`

`P(0) = 3610`

The initial investment was of $3,610.