You plan to retire in 30 years and would like to have $1,000,000 in investments. How much money would you have to invest today at a 7% annual interest rate compounded daily to reach your goal in 30 years? (Assume all years have 365 days. Round your answer to the nearest cent.)

To calculate how much you would need to invest today to reach $1,000,000 in 30 years with a 7% annual interest rate compounded daily, we can use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the future value (the amount you want, $1,000,000).
- $ P $ is the principal (the amount you invest today, which we are solving for).
- $ r $ is the annual interest rate (7% or 0.07).
- $ t $ is the time in years (30 years).
- $ n $ is the number of times the interest is compounded per year (365 for daily compounding).

Rearranging the formula to solve for $ P $:

\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]

Substitute the given values into the formula:

\[
P = \frac{1,000,000}{\left(1 + \frac{0.07}{365}\right)^{365 \times 30}}
\]

Now, let's calculate this value.You would need to invest **$122,481.09** today to reach $1,000,000 in 30 years with a 7% annual interest rate compounded daily.

Would you like further details on this calculation, or do you have any questions?

Here are 5 related questions to consider:
1. How does changing the interest rate affect the amount needed today?
2. What if the interest were compounded monthly instead of daily?
3. How would the investment change if you wanted to reach the goal in 25 years instead of 30?
4. What if you wanted to retire with $1,500,000 instead?
5. How would inflation impact your future value goal?

**Tip:** Compound interest grows faster the more frequently it's compounded, even with the same interest rate.

Discover how much you need to invest today to reach $1,000,000 in 30 years at a 7% interest rate compounded daily. This solution breaks down the compound interest formula step by step, providing insights into exponential growth and long-term financial planning. Ideal for advanced high school or college-level finance students.

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