You plan to retire in 35 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 35 years? (Assume all years have 365 days. Round your answer to the nearest cent.)


We can solve this problem using the formula for compound interest:

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

Where:
- $A$ is the future value (amount you want to reach, $1,000,000),
- $P$ is the present value (the amount you need to invest today),
- $r$ is the annual interest rate (7%, or 0.07),
- $n$ is the number of times interest is compounded per year (daily, so $n = 365$),
- $t$ is the time in years (35 years).

We need to solve for $P$, which represents the amount you need to invest today. Rearranging the formula for $P$:

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

Now, let's calculate this step by step.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through solving it manually, or is there something else you'd like to explore?

Here are five related questions you might be interested in:

1. What if the interest rate were compounded quarterly instead of daily?
2. How much would you need to invest today if the interest rate were 5% annually?
3. What would happen if you retired in 40 years instead of 35?
4. How much more would you need to invest if inflation was taken into account at 2% annually?
5. How does changing the compounding frequency affect the final amount?

**Tip:** Compound interest grows faster the more frequently it is compounded, even if the interest rate remains the same!

You plan to retire in 35 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 35 years? (Assume all years have 365 days. Round your answer to the nearest cent.)

Learn how to calculate the amount you need to invest today to reach $1,000,000 in 35 years with a 7% annual interest rate compounded daily. This problem explores compound interest, exponential growth, and key financial formulas. Ideal for high school seniors and college students.

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