Calculate the regular deposit made twice a year for 5 years at 6% compounded semi-annually(x2) to accumulate an amount of 4'000$ using this formula: Future Value= R[(1+i)^n-1/i].

To calculate the regular deposit (R) made semi-annually to accumulate an amount of $4,000 over 5 years at a 6% interest rate compounded semi-annually, we will use the given future value of an ordinary annuity formula:

\[
\text{Future Value} = R \left[ \frac{(1 + i)^n - 1}{i} \right]
\]

### Step-by-Step Solution:

1. **Identify the variables**:
   - **Future Value (FV)**: $4,000
   - **Interest rate per period (i)**: Since the interest is compounded semi-annually at a 6% annual rate, divide by 2:
     \[
     i = \frac{6\%}{2} = 3\% = 0.03
     \]
   - **Number of compounding periods (n)**: There are 2 deposits per year for 5 years, so:
     \[
     n = 2 \times 5 = 10
     \]

2. **Plug these values into the formula**:
   \[
   4000 = R \left[ \frac{(1 + 0.03)^{10} - 1}{0.03} \right]
   \]

3. **Calculate the term inside the brackets**:
   - First, calculate $ (1 + 0.03)^{10} $:
     \[
     (1.03)^{10} \approx 1.34392
     \]
   - Now, substitute this into the equation:
     \[
     4000 = R \left[ \frac{1.34392 - 1}{0.03} \right]
     \]

4. **Simplify the equation**:
   \[
   4000 = R \left[ \frac{0.34392}{0.03} \right]
   \]
   \[
   4000 = R \times 11.464
   \]

5. **Solve for $ R $**:
   \[
   R = \frac{4000}{11.464} \approx 348.85
   \]

### Answer:
The regular deposit made semi-annually should be approximately **$348.85**.

Would you like further details on any part of the solution?

Here are 5 related questions to expand on this topic:
1. How would the deposit amount change if the interest rate were compounded quarterly?
2. What is the impact on the deposit if the interest rate changes to 8%?
3. How would the calculation differ if the deposits were made annually instead of semi-annually?
4. What would be the total interest earned over the 5 years?
5. How can this formula be rearranged to solve for the future value given different deposit amounts?

**Tip:** When calculating compound interest, always remember to adjust the interest rate and periods to match the compounding frequency.

Calculate the regular deposit made twice a year for 5 years at 6% compounded semi-annually(x2) to accumulate an amount of 4,000$ using this formula: Future Value= R[(1+i)^n-1/i].

Learn how to calculate the regular deposit required to accumulate $4,000 over 5 years with a 6% interest rate compounded semi-annually. This step-by-step guide breaks down the compound interest formula and annuity calculation. Ideal for students in Grades 11-12 and college-level courses.

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