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To calculate the accumulated value of ten years of monthly payments of $1,000 with an interest rate of 4% compounded semi-annually, we need to use the formula for the future value of an annuity:

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

Where:
- $ A $ is the accumulated value.
- $ P = 1000 $ is the monthly payment.
- $ r = 0.04 $ is the annual interest rate.
- $ n = 2 $ is the number of compounding periods per year (since the interest is compounded semi-annually).
- $ t = 10 $ is the total number of years.

Since the payments are made monthly but interest is compounded semi-annually, we must account for this mismatch by first adjusting the effective rate of return for the semi-annual compounding.

Let me compute the value for you.The accumulated value after ten years of monthly payments of $1,000, with an interest rate of 4% compounded semi-annually, is approximately **$146,994.41**.

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

Here are 5 related questions you might find useful:
1. How does the formula for future value of an annuity change if compounding occurs quarterly?
2. What would happen to the accumulated value if the interest rate were 5% instead of 4%?
3. How would the result change if payments were made at the beginning of each month instead of at the end?
4. What is the effect of compounding frequency (monthly vs semi-annually) on the accumulated value?
5. How is the present value of an annuity calculated, and how does it differ from future value?

**Tip:** Always ensure to match the frequency of compounding and the frequency of payments when solving for annuities or loans!

Calculate the accumulated value after ten years of payments of $1000.00 made at the end of each month if interest is 4% compounded semi-annually.

Learn how to calculate the future value of an annuity after ten years with $1000 monthly payments and a 4% interest rate compounded semi-annually. Explore key financial formulas such as the future value of annuity and compounding theorem.

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