 Brady put money into an account that pays 4.1% interest compounded daily. After 8 years, he has $555.27. How much did he invest into the account? 

To solve this problem, we will use the **compound interest formula**:

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

Where:
- $ A $ is the amount of money after interest (final amount), which is $555.27.
- $ P $ is the principal (the initial amount invested) — this is what we are solving for.
- $ r $ is the annual interest rate in decimal form. For 4.1%, $ r = \frac{4.1}{100} = 0.041 $.
- $ n $ is the number of times the interest is compounded per year. Since it is compounded daily, $ n = 365 $.
- $ t $ is the time the money is invested or borrowed for, in years. Here, $ t = 8 $.

Now, we rearrange the formula to solve for $ P $:

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

Substituting the known values:

\[
P = \frac{555.27}{\left(1 + \frac{0.041}{365}\right)^{365 \times 8}}
\]

Let me calculate the value of $ P $.The initial investment Brady made into the account was approximately **$400.00**.

Would you like more details or have any further questions?

Here are five related questions to explore:
1. How would the initial investment change if the interest rate were 5% instead of 4.1%?
2. What if Brady had left the money for 10 years instead of 8? How would that affect the final amount?
3. What is the difference between daily compounding and monthly compounding in terms of final balance?
4. How much would Brady have after 8 years if he had invested $500 at the same rate?
5. How does the formula change if the interest is compounded continuously?

**Tip:** Small differences in the interest rate or the compounding period can significantly impact the final amount, especially over long periods.

Brady put money into an account that pays 4.1% interest compounded daily. After 8 years, he has $555.27. How much did he invest into the account?

Learn how to determine the initial investment for an account that grew to $555.27 over 8 years with 4.1% interest compounded daily. This detailed solution covers compound interest concepts and provides step-by-step calculations, suitable for Grades 9-12 students.

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