Lily invested $2,300 in an account paying an interest rate of 1, one eigth181​% compounded annually. Keilantra invested $2,300 in an account paying an interest rate of 0, one half021​% compounded monthly. After 8 years, how much more money would Lily have in her account than Keilantra, *to the nearest dollar*?

To determine how much more money Lily would have in her account than Keilantra after 8 years, we need to calculate the future value of both investments using the appropriate compounding formulas.

### Lily's Investment
Lily's investment is compounded annually. The formula for compound interest when compounded annually is:

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

Where:
- $ P $ is the principal amount,
- $ r $ is the annual interest rate (expressed as a decimal),
- $ n = 1 $ (since it's compounded annually),
- $ t $ is the time in years.

For Lily:
- $ P = 2300 $ dollars,
- $ r = 1.125\% = 0.01125 $,
- $ n = 1 $,
- $ t = 8 $ years.

So,

\[
A_{\text{Lily}} = 2300 \left(1 + \frac{0.01125}{1}\right)^{1 \cdot 8}
\]

### Keilantra's Investment
Keilantra's investment is compounded monthly. The formula for compound interest when compounded monthly is:

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

Where:
- $ P $ is the principal amount,
- $ r = 0.5\% = 0.005 $,
- $ n = 12 $ (since it's compounded monthly),
- $ t = 8 $ years.

So,

\[
A_{\text{Keilantra}} = 2300 \left(1 + \frac{0.005}{12}\right)^{12 \cdot 8}
\]

### Calculation
Let's compute the future values of both Lily's and Keilantra's investments, and then find the difference between them.After 8 years:

- **Lily's investment** grows to approximately **$2,515**.
- **Keilantra's investment** grows to approximately **$2,394**.

The difference between Lily's and Keilantra's accounts is **$121** (rounded to the nearest dollar). Therefore, Lily would have **$121 more** than Keilantra after 8 years.

Do you have any further questions or would you like more details?

Here are 5 related questions you might consider:
1. What would be the difference if both investments were compounded monthly?
2. How would the results change if the investment periods were longer, say 12 years?
3. How much would the difference be if the initial investment was $5,000 instead of $2,300?
4. What happens if the interest rates were slightly higher or lower?
5. How does the compounding frequency impact the total interest earned?

**Tip:** The frequency of compounding can significantly impact the amount of interest earned, even if the interest rate is low.

Discover how to calculate the future value of investments with compound interest. Solve the problem where Lily and Keilantra invested $2,300 each at different interest rates compounded annually and monthly, respectively, over 8 years. Lily's investment grows to approximately $2,515, while Keilantra's grows to approximately $2,394. Find out how much more money Lily would have compared to Keilantra after 8 years.

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