The million dollar question!
Allison is 18 years old and plans to retire at age 65 (in 47 years) with $1,000,000 in her retirement account. What amount would she have to set aside now in an investment paying 6% annual interest if the compounding is done daily (assume 365 days in a year)?


To determine how much Allison should invest today to reach $1,000,000 by the time she retires in 47 years, we can use the formula for compound interest:

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

Where:
- $A$ is the future value of the investment (in this case, $1,000,000),
- $P$ is the initial principal (the amount Allison invests today, which we're solving for),
- $r$ is the annual interest rate (6% or 0.06),
- $n$ is the number of times the interest is compounded per year (daily compounding, so $n = 365$),
- $t$ is the time in years (47 years).

Now, we solve for $P$:

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

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Meanwhile, here are some related questions:

1. How does the compounding frequency affect investment growth?
2. What would happen if the interest rate changed to 5%?
3. What would be the outcome if Allison started saving 10 years later?
4. How much more would Allison have if the interest compounded monthly instead of daily?
5. How do inflation and taxes affect retirement savings?

**Tip**: The earlier you start saving, the more powerful the compounding effect becomes, even with small contributions!

Allison is 18 years old and plans to retire at age 65 (in 47 years) with $1,000,000 in her retirement account. What amount would she have to set aside now in an investment paying 6% annual interest if the compounding is done daily (assume 365 days in a year)?

Discover how much Allison needs to invest today to reach $1,000,000 by retirement in 47 years with a 6% annual interest rate and daily compounding. Learn how the compound interest formula is used to calculate initial investments. Suitable for high school seniors and early college students.

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