https://file.aiquickdraw.com/mathbot/file/1727888637316aim1f3x4.jpg

The problem in the image is asking to calculate the amount of interest earned on a deposit of $11,000 over 9 years at an annual interest rate of 10%, with the interest compounded quarterly.

### The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $A$ = the final amount (principal + interest)
- $P$ = the initial principal (in this case, $11,000)
- $r$ = annual interest rate (as a decimal, so 10% = 0.10)
- $n$ = number of times the interest is compounded per year (quarterly means $n = 4$)
- $t$ = the time the money is invested for (in years, here 9 years)

### Step 1: Plug in the given values:
\[
A = 11000 \left(1 + \frac{0.10}{4}\right)^{4 \times 9}
\]
\[
A = 11000 \left(1 + 0.025\right)^{36}
\]
\[
A = 11000 \left(1.025\right)^{36}
\]

### Step 2: Calculate the exponent:
\[
1.025^{36} \approx 2.20804
\]

### Step 3: Multiply by the principal:
\[
A = 11000 \times 2.20804 \approx 24,288.44
\]

### Step 4: Calculate the interest earned:
\[
\text{Interest} = A - P = 24,288.44 - 11,000 = 13,288.44
\]

So, the amount of interest earned is approximately **$13,288.44**.

Would you like further details or have any questions?

Here are five related questions for further exploration:
1. How would the result change if the interest were compounded monthly instead of quarterly?
2. What if the interest rate was 8% instead of 10%?
3. How would the calculation differ if the interest were compounded annually?
4. How long would it take for the investment to double at the same interest rate?
5. What is the total amount (principal + interest) after 9 years?

**Tip:** Compounding more frequently (e.g., quarterly, monthly) generally increases the amount of interest earned compared to annual compounding.

Calculate the amount of interest earned (in dollars) in 9 years on $11,000 deposited in an account paying 10% annual interest, compounded quarterly.

Learn how to calculate compound interest on a $11,000 deposit at a 10% annual interest rate compounded quarterly over 9 years. This problem covers the compound interest formula and exponential growth concepts. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation