Samantha invested $50,000 in an account paying an interest rate of 4.1% compounded daily. Assuming no deposits or withdrawals are made, how much money, *to the nearest ten dollars*, would be in the account after 8 years?

To solve this problem, we'll use the formula for compound interest:

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

Where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested or borrowed for, in years.

Given:
- $ P = 50,000 $
- $ r = 4.1\% = 0.041 $
- $ n = 365 $ (since the interest is compounded daily)
- $ t = 8 $ years

Now, we substitute these values into the formula:

\[
A = 50,000 \left(1 + \frac{0.041}{365}\right)^{365 \times 8}
\]

Let's calculate this.After 8 years, Samantha would have approximately **$69,410** in the account, rounded to the nearest ten dollars.

Would you like more details or have any questions? 

Here are 5 related questions you might find interesting:
1. What would the amount be if the interest were compounded monthly instead of daily?
2. How does the final amount change if the interest rate increases to 5%?
3. What would be the amount after 8 years if Samantha had initially invested $100,000 instead of $50,000?
4. How long would it take for the investment to double at the same interest rate with daily compounding?
5. What is the difference in the final amount if the interest is compounded annually instead of daily?

**Tip:** Compounding frequency significantly affects the final amount. The more frequent the compounding, the higher the accumulated amount over time.

Learn how to calculate compound interest with daily compounding for a $50,000 investment at an annual interest rate of 4.1% over 8 years. Get the precise amount, rounded to the nearest ten dollars. Explore related scenarios and calculations.

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