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 determine how much more David will have in the account with the higher interest rate after 3 years, we can use the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (the initial investment).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times the interest is compounded per year (for this problem, $ n = 1 $ since the interest is compounded annually).
- $ t $ is the time the money is invested for (in years).

### Account 1: 2% interest compounded annually
- $ P = 2,000 $
- $ r = 0.02 $
- $ n = 1 $
- $ t = 3 $

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

### Account 2: 1.5% interest compounded annually
- $ P = 2,000 $
- $ r = 0.015 $
- $ n = 1 $
- $ t = 3 $

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

Now let's calculate these amounts.After 3 years:
- The account with the 2% interest rate will have $ 2,122.42 $.
- The account with the 1.5% interest rate will have $ 2,091.36 $.

Thus, David will have **\$31.06** more in the account with the higher interest rate.

Would you like further details or have any questions?

Here are 5 related questions you could explore:
1. What happens if the interest is compounded monthly instead of annually?
2. How much will David have in both accounts after 5 years?
3. What is the total interest earned from both accounts after 3 years?
4. How would the final amount change if the initial investment were \$3,000 instead of \$2,000?
5. How does the difference grow over a longer period, like 10 years?

**Tip:** Compounding more frequently leads to greater accumulated interest 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 much more David will earn in an account with a 2% annual interest rate, compounded annually, compared to an account with 1.5%. Detailed solution shows the step-by-step process of using the compound interest formula. Ideal for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation