
How much interest is earned in 9 years on $8600 deposited in an account paying 5% interest, compounded semiannually?

To calculate the interest earned on a deposit compounded semiannually, we use the compound interest formula:

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

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

### Given:
- $P = 8600$,
- $r = 5\% = 0.05$,
- $n = 2$ (since it’s compounded semiannually),
- $t = 9$ years.

Let's plug these values into the formula to calculate the total amount, $A$.

\[
A = 8600 \left(1 + \frac{0.05}{2}\right)^{2 \times 9}
\]

After calculating $A$, we can find the interest earned by subtracting the principal from the total amount:

\[
\text{Interest Earned} = A - P
\]

I'll calculate this now.The total amount in the account after 9 years will be approximately \$13,413.06. The interest earned over the 9 years is approximately **\$4,813.06**.

Would you like any further details or explanations?

Here are 5 related questions:
1. How would the interest change if the rate were compounded quarterly?
2. What would the interest be if the interest rate was 6% instead of 5%?
3. How much interest would you earn if the money was deposited for only 5 years?
4. How would the formula change if the interest was compounded monthly?
5. What is the difference between simple and compound interest over the same period?

**Tip:** Always confirm how frequently interest is compounded, as it significantly affects the final amount.

How much interest is earned in 9 years on $8600 deposited in an account paying 5% interest, compounded semiannually?

Learn how to calculate the interest earned on a deposit of $8600 at 5% interest, compounded semiannually over 9 years. This guide includes a step-by-step solution using the compound interest formula and is suitable for students in 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