Jan invests $3,000 at the beginning of each year for 30 years. The annual return is 12%. We want to find the total amount she will have at the end of 30 years, rounding the answer down to the nearest whole number.

1. Problem Description

Jan invests $3,000 at the beginning of each year for 30 years. The annual return is 12%. We want to find the total amount she will have at the end of 30 years, rounding the answer down to the nearest whole number.

2. Solution Steps

This is an annuity due problem. The formula for the future value of an annuity due is:

$FV = P * \frac{((1 + r)^n - 1)}{r} * (1 + r)$

Where:

$FV$ is the future value of the annuity

$P$ is the periodic payment ($3,000)

$r$ is the interest rate (0.12)

$n$ is the number of periods (30)

Plugging in the values:

$FV = 3000 * \frac{((1 + 0.12)^{30} - 1)}{0.12} * (1 + 0.12)$

$FV = 3000 * \frac{(1.12^{30} - 1)}{0.12} * 1.12$

$FV = 3000 * \frac{(29.959922 - 1)}{0.12} * 1.12$

$FV = 3000 * \frac{28.959922}{0.12} * 1.12$

$FV = 3000 * 241.332683 * 1.12$

$FV = 3000 * 270.292605$

$FV = 810877.815$

Rounding down to the nearest whole number, we get

8

1

0

8

7

7.

3. Final Answer

810877