Find the future value of an ordinary annuity of $4,000 paid quarterly for 2 years, if the interest rate is 8%, compounded quarterly. (Round your answer to the nearest cent.)


To find the future value of an ordinary annuity, we use the formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

where:
- $ P $ is the payment amount per period,
- $ r $ is the interest rate per period,
- $ n $ is the total number of payments.

### Given Data:
- **Payment amount per period ( $ P $ ):** $4,000
- **Interest rate (annual):** 8%
- **Compounding frequency:** Quarterly
- **Time period:** 2 years

### Step-by-Step Solution:

1. **Determine the interest rate per period ($ r $)**:
   - Annual interest rate = 8%, so quarterly rate = $ \frac{8\%}{4} = 2\% = 0.02 $.

2. **Determine the total number of payments ( $ n $ )**:
   - 2 years with quarterly payments: $ 2 \times 4 = 8 $ payments.

3. **Plug values into the formula**:

   \[
   FV = 4000 \times \frac{(1 + 0.02)^8 - 1}{0.02}
   \]

4. **Calculate each part**:

   - $ (1 + 0.02)^8 = 1.171659 $
   - Subtract 1: $ 1.171659 - 1 = 0.171659 $
   - Divide by $ r $: $ \frac{0.171659}{0.02} = 8.58295 $
   - Multiply by $ P $: $ 4000 \times 8.58295 = 34331.80 $

### Final Answer:

The future value of the annuity is approximately **$34,331.80**.

---

Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would the future value change if the payments were made monthly instead of quarterly?
2. What if the interest rate were compounded monthly at the same annual rate?
3. How is the formula adjusted for an annuity due rather than an ordinary annuity?
4. What impact does increasing the payment amount have on the future value?
5. How does changing the interest rate affect the future value of the annuity?

**Tip:** For ordinary annuities, payments are made at the end of each period, so ensure the formula used aligns with the timing of payments.

Find the future value of an ordinary annuity of $4,000 paid quarterly for 2 years, if the interest rate is 8%, compounded quarterly. (Round your answer to the nearest cent.)

Learn how to calculate the future value of an ordinary annuity with $4,000 quarterly payments over 2 years at an 8% interest rate compounded quarterly. This detailed solution covers the future value of annuities, compound interest, and financial formulas. Ideal for high school students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation