Principal $15,000, 2 years, rate 8%, compounded quarterly. What’s the amount and interest

To calculate the total amount $ A $ and the interest earned on a principal of $15,000 compounded quarterly at an annual interest rate of 8% for 2 years, we can use the compound interest formula:

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

Where:
- $ A $ is the amount (principal + interest),
- $ P = 15,000 $ is the principal,
- $ r = 0.08 $ is the annual interest rate (8%),
- $ n = 4 $ is the number of times the interest is compounded per year (quarterly),
- $ t = 2 $ is the time the money is invested for (in years).

### Step 1: Plug in the values

\[
A = 15,000 \left( 1 + \frac{0.08}{4} \right)^{4 \times 2}
\]

### Step 2: Simplify the expression

\[
A = 15,000 \left( 1 + 0.02 \right)^{8}
\]
\[
A = 15,000 \left( 1.02 \right)^{8}
\]

### Step 3: Calculate $ A $

\[
A = 15,000 \times 1.171659
\]
\[
A \approx 17,574.88
\]

### Step 4: Calculate the interest earned

The interest earned $ I $ is:

\[
I = A - P = 17,574.88 - 15,000 = 2,574.88
\]

### Final Answer:
- **Amount**: $17,574.88
- **Interest**: $2,574.88

Would you like further clarification on the steps, or have any other questions?

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Here are 5 related questions:
1. What would the amount be if the interest rate was compounded monthly?
2. How would the total amount change if the rate was 6% instead of 8%?
3. What is the difference between simple interest and compound interest?
4. How does the frequency of compounding affect the final amount?
5. How would the formula change if the compounding were done continuously?

**Tip**: The more frequent the compounding, the greater the amount of interest earned.

Principal $15,000, 2 years, rate 8%, compounded quarterly. What’s the amount and interest?

Learn how to calculate the total amount and interest for a $15,000 principal invested at 8% interest, compounded quarterly over 2 years. This step-by-step solution walks through using the compound interest formula, resulting in an amount of $17,574.88 and $2,574.88 in interest. Suitable for Grades 9-12.

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