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The question you posted is about calculating the accumulated value of an Ordinary General Annuity where:

- Payments of **$1,000** are made **at the end of each month**.
- The **interest rate** is **4% compounded semi-annually**.
- The term is **10 years**.
- The problem specifies we first need to find the value of **'c'** (the interest rate per period), and then find the value of **'p'** (the accumulated value).

### Step 1: Calculate the interest rate per period $ c $

Since the interest is compounded semi-annually, we first need to determine the **monthly interest rate**.

1. The annual nominal interest rate is 4%, but it is compounded semi-annually. This means the **semi-annual rate** is:
   \[
   \text{Semi-annual rate} = \frac{4\%}{2} = 2\%
   \]
   So, the semi-annual interest rate is **0.02**.

2. We need to convert this to a monthly interest rate. The monthly interest rate is found by taking the 6th root of the semi-annual interest rate (since there are 6 months in a semi-annual period):
   \[
   \text{Monthly interest rate} = \left( 1 + 0.02 \right)^{\frac{1}{6}} - 1
   \]

### Step 2: Calculate the number of periods $ N $

The number of monthly payments over 10 years is:
\[
N = 10 \times 12 = 120 \text{ months}
\]

### Step 3: Use the future value of an ordinary annuity formula

For an ordinary annuity, the future value $ A $ is given by the formula:
\[
A = P \times \frac{(1 + c)^N - 1}{c}
\]
Where:
- $ P = 1000 $ (the monthly payment),
- $ c $ is the monthly interest rate (we will calculate this),
- $ N = 120 $.

Let me now compute the value of $ A $ using these formulas.The accumulated value of the annuity after 10 years of monthly payments of $1,000 at the end of each month, with an interest rate of 4% compounded semi-annually, is approximately **$146,994.41**.

Would you like further details or clarifications on any steps?

Here are some related questions to expand your understanding:
1. How would the result change if the interest rate were compounded quarterly instead of semi-annually?
2. What would happen to the accumulated value if the payments were made at the beginning of each month (i.e., an annuity due)?
3. How can the formula be adjusted for different payment frequencies, like quarterly or bi-monthly?
4. What is the difference between simple and compound interest in terms of annuities?
5. How would a variable interest rate affect the future value of an annuity?

**Tip:** When dealing with annuities, be sure to carefully distinguish between annuities due (payments at the beginning of each period) and ordinary annuities (payments at the

Calculate the accumulated value after ten years of payments of $1,000.00 made at the end of each month if interest is 4% compounded semi-annually. (Note: This is an Ordinary General Annuity; therefore, find the value of 'c' first and then find the value of 'p'.)

Learn how to calculate the future value of an ordinary annuity with monthly payments of $1,000 over 10 years, compounded semi-annually at 4%. Understand key concepts like the annuity formula and compound interest.

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