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.