Benjamin invested $20,000 in an account paying an interest rate of 7 5/8% compounded monthly. Kehlani invested $20,000 in an account paying an interest rate of 7 3/4% compounded quarterly. After 10 years, how much more money would Kehlani have in her account than Benjamin, to the nearest dollar?

To solve this problem, let's correct and clarify the interest rates given in the question:

- Benjamin's interest rate: $7 \frac{5}{8}\%$ = $7 + \frac{5}{8}\%$ = $7.625\%$
- Kehlani's interest rate: $7 \frac{3}{4}\%$ = $7 + \frac{3}{4}\%$ = $7.75\%$

We will use the compound interest formula to calculate the future value for both Benjamin and Kehlani.

### Step 1: Calculate Benjamin's Future Value
- Principal $ P = 20,000 $ dollars
- Annual interest rate $ r = 7.625\% = 0.07625 $
- Compounded monthly: $ n = 12 $
- Time $ t = 10 $ years

The future value $ A_B $ for Benjamin is:

\[
A_B = 20000 \left(1 + \frac{0.07625}{12}\right)^{12 \times 10}
\]

### Step 2: Calculate Kehlani's Future Value
- Principal $ P = 20,000 $ dollars
- Annual interest rate $ r = 7.75\% = 0.0775 $
- Compounded quarterly: $ n = 4 $
- Time $ t = 10 $ years

The future value $ A_K $ for Kehlani is:

\[
A_K = 20000 \left(1 + \frac{0.0775}{4}\right)^{4 \times 10}
\]

### Step 3: Compute the Difference
The difference between Kehlani's and Benjamin's future value is:

\[
\text{Difference} = A_K - A_B
\]

Let's calculate these values.After 10 years, Kehlani would have approximately **$322** more in her account than Benjamin, to the nearest dollar.

Would you like more details or have any questions about these calculations?

Here are 8 related questions you might find useful:
1. How does the effect of compounding frequency differ for different interest rates?
2. What is the impact of increasing the investment period to 20 years for both Benjamin and Kehlani?
3. How would the final difference change if both investments were compounded annually instead?
4. What is the effect of changing the principal amount on the future value?
5. Can you explain how the compound interest formula is derived?
6. What would be the outcome if both investments had the same interest rate but different compounding frequencies?
7. How would inflation affect the real value of these investments after 10 years?
8. What is the difference in future value if Kehlani's interest rate was 8% instead of 7.75%?

**Tip:** Small differences in interest rates or compounding frequencies can lead to noticeable differences in the final amount over time. Always compare both aspects when evaluating investment options.

Learn how to calculate future values with compound interest rates for Benjamin and Kehlani's investments. Understand the impact of different interest rates and compounding frequencies over 10 years. Benjamin invested $20,000 at 7.625% compounded monthly, while Kehlani invested $20,000 at 7.75% compounded quarterly. After 10 years, find out how much more Kehlani would have in her account compared to Benjamin.

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