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.