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 how much more David will have in the account with the higher interest rate, we need to calculate the future value of both accounts after 3 years. Since both accounts are compounded annually, we can use the compound interest formula:

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

Where:
- $ A $ is the amount after interest,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate,
- $ 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 a 2% interest rate

For the account with a 2% interest rate:
- $ P = 2000 $
- $ r = 0.02 $
- $ n = 1 $
- $ t = 3 $

\[
A_1 = 2000 \left( 1 + \frac{0.02}{1} \right)^{1 \times 3} = 2000 \left( 1.02 \right)^3
\]

### Step 2: Calculate the amount for the account with a 1.5% interest rate

For the account with a 1.5% interest rate:
- $ P = 2000 $
- $ r = 0.015 $
- $ n = 1 $
- $ t = 3 $

\[
A_2 = 2000 \left( 1 + \frac{0.015}{1} \right)^{1 \times 3} = 2000 \left( 1.015 \right)^3
\]

### Step 3: Find the difference between the two amounts

The difference is:

\[
\text{Difference} = A_1 - A_2
\]

Let me compute these values for you.After 3 years:
- The amount in the account with a 2% interest rate will be \$2,122.42.
- The amount in the account with a 1.5% interest rate will be \$2,091.36.

The difference between the two accounts will be approximately **\$31.06**, meaning David will have \$31.06 more in the account with the higher interest rate.

Would you like further details or explanations?

Here are five related questions for deeper understanding:
1. How would the difference change if the interest rates were compounded quarterly instead of annually?
2. What if the investment period was 5 years instead of 3 years? How much would the difference be?
3. How does the compound interest formula differ from simple interest?
4. What happens to the total amount if the initial investment was doubled?
5. How does the difference scale with longer investment periods?

**Tip**: The more frequently interest is compounded, the greater the effect of compounding over time.

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?

Explore how to calculate and compare compound interest between two accounts with different interest rates (2% and 1.5%) over 3 years. Find out how much more David will earn in the account with the higher interest rate using the compound interest formula. This problem is ideal for students in Grades 9-12.

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