A couple pays $600 at the end of each 6 months for 4 years into an ordinary annuity paying 6% compounded semiannually. What is the future value at the end of 4 years? (Use either the TVM solver or the appropriate formula to solve. Round your final answer to two decimal places.)

We can use the future value formula for an ordinary annuity to solve this problem. The formula is:

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

Where:
- $FV$ is the future value of the annuity.
- $P$ is the payment made each period ($600 in this case).
- $i$ is the interest rate per period.
- $n$ is the total number of periods.

### Step 1: Determine the values
- $P = 600$
- The annual interest rate is 6%, but it is compounded semiannually, so the interest rate per period is $ \frac{6\%}{2} = 3\% = 0.03 $.
- The number of periods is $ 4 \text{ years} \times 2 \text{ periods per year} = 8 \text{ periods} $.

### Step 2: Plug values into the formula
We can now calculate the future value:

\[
FV = 600 \times \frac{(1 + 0.03)^8 - 1}{0.03}
\]

Let me calculate this for you.The future value of the ordinary annuity at the end of 4 years is approximately **$5335.40**.

Do you want more details on the calculation or have any other questions?

Here are 5 related questions to expand on this topic:
1. How would the future value change if the interest rate were compounded quarterly instead of semiannually?
2. What would be the future value if payments were made at the beginning of each period (annuity due)?
3. How does the length of the annuity affect the future value if the payment and interest rates remain constant?
4. How can we calculate the present value of an ordinary annuity with the same conditions?
5. How would the future value be affected if the couple made larger payments over the same period?

**Tip:** An ordinary annuity makes payments at the end of each period, while an annuity due makes payments at the beginning, affecting the future value.

Find the future value of an ordinary annuity where a couple makes $600 payments every 6 months for 4 years, with 6% interest compounded semiannually. This problem explores the future value formula, time value of money concepts, and is suitable 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