To determine how much more money Lily would have than Keilantra after 8 years, we'll calculate the future value of both investments using the formula for compound interest:

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

Where:

• $A$ is the future value of the investment.
• $P$ is the principal amount ($2300$).
• $r$ is the annual interest rate (as a decimal).
• $n$ is the number of times interest is compounded per year.
• $t$ is the number of years.

Step 1: Calculate Lily's investment

Lily's annual interest rate: $1\frac{1}{8}\%$ = $0.01125$ as a decimal. Interest is compounded annually ($n = 1$).

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

Step 2: Calculate Keilantra's investment

Keilantra's annual interest rate: $0.5\%$ = $0.005$ as a decimal. Interest is compounded monthly ($n = 12$).

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

Step 3: Compare the two investments

Now, let’s compute the exact amounts.# Variables for the calculations P = 2300 # Principal amount t = 8 # Time in years

Lily's investment details

r_lily = 0.01125 # Annual interest rate for Lily n_lily = 1 # Compounded annually

Keilantra's investment details

r_keilantra = 0.005 # Annual interest rate for Keilantra n_keilantra = 12 # Compounded monthly

Calculate future values

A_lily = P * (1 + r_lily / n_lily) ** (n_lily * t) A_keilantra = P * (1 + r_keilantra / n_keilantra) ** (n_keilantra * t)

Difference in amounts

difference = A_lily - A_keilantra

A_lily, A_keilantra, round(difference)(2515.3366163123465, 2393.8448373920323, 121)(2515.3366163123465, 2393.8448373920323, 121)successAfter 8 years:

• Lily's account balance: $2,515
• Keilantra's account balance: $2,394

The difference is approximately $121. Lily has $121 more than Keilantra.

Do you want further details or have questions? Here are some related questions for exploration:

1. How does the frequency of compounding affect the growth of an investment?
2. What would happen if Lily and Keilantra both invested for 10 years instead of 8?
3. How does the interest rate impact the overall difference in the accounts after 8 years?
4. What is the effect of a principal increase (e.g., $5,000 instead of $2,300)?
5. Can we determine the breakeven point for both accounts (if they exist)?

Tip: Compounding more frequently generally leads to higher returns, even at lower interest rates.