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 calculate the future value of each account using the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after interest,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (in decimal form),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the time the money is invested (in years).

Since the interest is compounded annually in both accounts, $ n = 1 $. Let's calculate the future value for each account after 3 years.

### 1st Account (2% interest):
\[
A_1 = 2000(1 + \frac{0.02}{1})^{1 \times 3} = 2000(1.02)^3
\]

\[
A_1 = 2000 \times 1.061208 = 2122.42
\]

### 2nd Account (1.5% interest):
\[
A_2 = 2000(1 + \frac{0.015}{1})^{1 \times 3} = 2000(1.015)^3
\]

\[
A_2 = 2000 \times 1.045681 = 2091.36
\]

### Difference:
Now, subtract the amount in the second account from the amount in the first account:

\[
\text{Difference} = A_1 - A_2 = 2122.42 - 2091.36 = 31.06
\]

David will have **$31.06 more** in the account with the higher interest rate after 3 years.

---

Would you like more details or have any further questions? Here are some related questions you may explore:

1. How would the result change if the interest were compounded monthly instead of annually?
2. What would the total difference be after 5 years instead of 3?
3. How much interest would David earn in total after 3 years for both accounts?
4. How does the future value formula change with continuous compounding?
5. What is the impact of different compounding periods on long-term investments?

**Tip:** Compound interest grows faster as the frequency of compounding periods increases (e.g., monthly vs. annually).

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?

Discover how to calculate the difference in compound interest for two accounts, one at 2% and the other at 1.5% interest, both compounded annually. This problem breaks down the calculation step-by-step and highlights key financial math concepts. Ideal for high school students in Grades 9-12.

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