David invested $2,000 in an account with an annual interest rate of 2%, compounded annually, and another $2,000 in an account with an annual interest rate of 1.5%, compounded annually.
After 3 years, how much more will David have in the account with the higher interest rate?

To find out how much more David will have in the account with the higher interest rate after 3 years, we need to apply the formula for compound interest:

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

where:
- $A$ is the amount in the account after interest.
- $P$ is the principal (initial investment).
- $r$ is the annual interest rate (as a decimal).
- $n$ is the number of times the interest is compounded per year (since it's compounded annually, $n = 1$).
- $t$ is the time in years.

### Step 1: Calculate the amount for the account with 2% interest.
Here:
- $P = 2000$
- $r = 0.02$
- $n = 1$
- $t = 3$

Using the formula:
\[
A_1 = 2000 \left( 1 + \frac{0.02}{1} \right)^{1 \times 3} = 2000 \left( 1.02 \right)^3
\]
\[
A_1 = 2000 \times 1.061208 = 2122.42
\]

### Step 2: Calculate the amount for the account with 1.5% interest.
Here:
- $P = 2000$
- $r = 0.015$
- $n = 1$
- $t = 3$

Using the formula:
\[
A_2 = 2000 \left( 1 + \frac{0.015}{1} \right)^{1 \times 3} = 2000 \left( 1.015 \right)^3
\]
\[
A_2 = 2000 \times 1.04568 = 2091.36
\]

### Step 3: Calculate the difference.
\[
\text{Difference} = A_1 - A_2 = 2122.42 - 2091.36 = 31.06
\]

### Conclusion:
After 3 years, David will have **$31.06 more** in the account with the 2% interest rate compared to the account with the 1.5% interest rate.

---

Would you like a breakdown of any step or further details? Here are some related questions for additional practice:

1. What would happen if the compounding period were semi-annual instead of annual?
2. How would the result change if the investment period were extended to 5 years?
3. How does increasing the principal affect the final outcome?
4. What if the interest rate on the second account was compounded monthly?
5. How does the effect of interest rates change if both accounts had different initial investments?

**Tip:** Small differences in interest rates can make a significant difference in returns over time, especially with compound interest.

David invested $2,000 in an account with an annual interest rate of 2%, compounded annually, and another $2,000 in an account with an annual interest rate of 1.5%, compounded annually. After 3 years, how much more will David have in the account with the higher interest rate?

Calculate how much more David will have in an account with a 2% annual interest rate compared to an account with a 1.5% annual interest rate after 3 years, using the compound interest formula. This example shows the difference in returns due to small variations in interest rates, suitable for Grades 9-12.

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