Let's compute the balance for Kio's investment after 30 years using 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 for in years.

For Kio:

• $P = 1200$
• $r = 4.25\% = 0.0425$
• $n = 1$ (since the interest is compounded annually)
• $t = 30$ years

Substitute the values into the formula:

$A = 1200 \left(1 + \frac{0.0425}{1}\right)^{1 \times 30}$ $A = 1200 \left(1 + 0.0425\right)^{30}$ $A = 1200 \left(1.0425\right)^{30}$

Now, let's calculate this step by step:

$A \approx 1200 \times 3.281030071$ $A \approx 3937.24$

Thus, after 30 years, Kio will have approximately $3937.24 in the account.

Discussion of the Difference:

After 10 years:

• Chang: $1776.29
• Kio: $1822.85

After 30 years:

• Chang: $3892.08
• Kio: $3937.24

Even though the difference in interest rates is small (4.0% vs. 4.25%), over time it significantly impacts the final balances due to the effect of compounding. After 30 years, Kio's balance is about $45.16 higher than Chang's. This demonstrates how even a slight increase in the interest rate can lead to substantial differences in long-term savings.

Do you want more details or have any questions?

Here are five related questions you might find useful:

1. How would the balances change if the interest was compounded quarterly instead of annually?
2. What would the balances be if both had invested $1500 instead of $1200?
3. How would a decrease in the interest rate by 0.5% affect the final amount?
4. What is the formula for continuous compounding, and how would it affect these scenarios?
5. How does inflation impact the real value of these investments over 30 years?

Tip: When comparing savings plans, always consider how the interest rate and compounding frequency affect long-term growth. Small differences can lead to significant disparities over time.