How much should be deposited into an account semiannually to have a balance of $9,500 in eight years if the rate is 1.25% compounded semiannually?

To solve this problem, we need to calculate the regular semiannual deposit (denoted as $ D $) that should be made into an account in order to accumulate to a future value of $9,500 over 8 years, with an interest rate of 1.25% compounded semiannually.

We can use the **future value of an ordinary annuity** formula:

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

Where:
- $ FV $ is the future value, which is $9,500,
- $ D $ is the regular deposit (what we're solving for),
- $ r $ is the interest rate per period,
- $ n $ is the total number of periods.

### Step 1: Determine the variables
- The interest rate per period $ r $ is the annual interest rate divided by the number of compounding periods per year. Since the interest is compounded semiannually, we divide 1.25% by 2:
  \[
  r = \frac{1.25\%}{2} = 0.00625
  \]
- The number of periods $ n $ is the number of years times the number of compounding periods per year. Since we have 8 years and semiannual compounding:
  \[
  n = 8 \times 2 = 16
  \]

### Step 2: Use the formula
Now, substitute the known values into the future value formula:

\[
9,500 = D \times \frac{(1 + 0.00625)^{16} - 1}{0.00625}
\]

### Step 3: Solve for $ D $
Let's calculate $ D $.The regular semiannual deposit that should be made is approximately **$566.41**.

Would you like further details or have any questions? Here are some related questions you might explore:

1. How would the required deposit change if the interest rate were higher?
2. What if the deposits were made annually instead of semiannually?
3. How does the time period affect the required deposit?
4. What would the total amount of deposits be after 8 years?
5. How does the formula change for continuous compounding?

**Tip:** The frequency of compounding significantly affects the future value of investments, so it's crucial to consider how often interest is compounded when making financial plans.

Discover how to calculate the regular semiannual deposit needed to accumulate $9,500 in eight years with a 1.25% interest rate compounded semiannually. This detailed guide walks through the use of the future value of an annuity formula to solve this financial problem.

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