Charlotte invested $730 in an account paying an interest rate of 3, one half3
2
1
​
% compounded continuously. Khalil invested $730 in an account paying an interest rate of 3, start fraction, 7, divided by, 8, end fraction3
8
7
​
% compounded daily. After 8 years, how much more money would Khalil have in his account than Charlotte, to the nearest dollar?

To solve this problem, we will calculate the amount of money in Charlotte's and Khalil's accounts after 8 years, using the respective interest rates and compounding methods.

### Charlotte's Account:
- Principal: $ P = 730 $
- Interest rate: $ r = 3.5\% = 0.035 $ (since 3$\frac{1}{2}$% = 3.5%)
- Time: $ t = 8 $ years
- Compounding: Continuously

For continuous compounding, the formula is:
\[
A = P \cdot e^{rt}
\]
Where:
- $ P $ is the principal
- $ r $ is the interest rate (in decimal)
- $ t $ is the time in years
- $ e $ is Euler's number (approximately 2.71828)

Plugging in the values for Charlotte:
\[
A_C = 730 \cdot e^{0.035 \cdot 8}
\]

### Khalil's Account:
- Principal: $ P = 730 $
- Interest rate: $ r = \frac{7}{8}\% = 0.0375 $ (since $\frac{7}{8}$% = 0.875%)
- Time: $ t = 8 $ years
- Compounding: Daily (365 times a year)

For daily compounding, the formula is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $ P $ is the principal
- $ r $ is the interest rate (in decimal)
- $ t $ is the time in years
- $ n $ is the number of times the interest is compounded per year

Plugging in the values for Khalil:
\[
A_K = 730 \left(1 + \frac{0.0375}{365}\right)^{365 \cdot 8}
\]

Now, let's calculate both amounts and find the difference.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can walk you through the steps to calculate it manually. Let me know if you'd like assistance with that!

Here are 5 related questions you might find interesting:
1. What are the differences between continuous and daily compounding interest methods?
2. How does the interest rate affect compound growth over long periods of time?
3. How can we use the compound interest formula for quarterly compounding?
4. What is the significance of Euler's number in continuous compounding?
5. How can the number of compounding periods per year impact overall returns?

**Tip**: When comparing two investments, small differences in interest rates or compounding frequency can lead to significant differences in returns over time.

Charlotte invested $730 in an account paying an interest rate of 3.5% compounded continuously. Khalil invested $730 in an account paying an interest rate of 3.875% compounded daily. After 8 years, how much more money would Khalil have in his account than Charlotte, to the nearest dollar?

Compare two investments of $730 over 8 years: one compounded continuously at 3.5% and another compounded daily at 3.875%. Learn how to use compound interest formulas to calculate final amounts and find out how much more one account earns. Suitable for high school students learning about compound interest.

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