Edgar has $7,000 in an account that earns 15% interest compounded annually.
To the nearest cent, how much interest will he earn in 3 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
$


To solve this problem, we can use the compound interest formula:

\[
B = p(1 + r)^t
\]

where:
- $ B $ is the balance (final amount)
- $ p $ is the principal (starting amount), which is $7,000
- $ r $ is the interest rate expressed as a decimal, which is 15%, or 0.15
- $ t $ is the time in years, which is 3 years

First, let's plug the values into the formula:

\[
B = 7000 \times (1 + 0.15)^3
\]

Now, simplify step by step:

\[
B = 7000 \times (1.15)^3
\]

Calculating $ (1.15)^3 $:

\[
1.15^3 = 1.520875
\]

Now, multiply by the principal:

\[
B = 7000 \times 1.520875 = 10646.125
\]

So, the final balance $ B $ is $10,646.13 (rounded to the nearest cent).

To find the interest earned, subtract the initial principal from the final balance:

\[
\text{Interest} = B - p = 10646.13 - 7000 = 3646.13
\]

Therefore, the interest Edgar will earn in 3 years is **$3,646.13**.

Would you like more details or have any questions?

### Related Questions:
1. How would the result change if the interest were compounded quarterly instead of annually?
2. What would the interest be if Edgar left the money in the account for 5 years instead of 3?
3. How much interest would Edgar earn in 3 years if the interest rate was 10% instead of 15%?
4. How can we calculate the interest earned if the compounding period is monthly?
5. What is the future value if the interest rate is compounded continuously?

### Tip:
When dealing with compound interest, always ensure that the interest rate and compounding period are aligned (e.g., for annual interest, use annual compounding).

Edgar has $7,000 in an account that earns 15% interest compounded annually. To the nearest cent, how much interest will he earn in 3 years? Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Learn how to calculate the interest earned on $7,000 at 15% compounded annually over 3 years. This step-by-step solution uses the compound interest formula and demonstrates how to find the final balance and interest. Suitable 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