Find the future value for the ordinary annuity with the given payment and interest rate.
PMT = $850; 1.05% compounded semiannually for 6 years.
The future value of the ordinary annuity is $

To find the future value (FV) of an ordinary annuity, we can use the following formula:

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

Where:
- $ PMT $ is the payment made each period.
- $ r $ is the interest rate per period.
- $ n $ is the total number of periods.

### Given:
- $ PMT = 850 $
- Interest rate per year ($ i = 1.05\% $) compounded semiannually.
- Duration = 6 years.

### Step-by-step Calculation:

1. **Convert annual interest rate to semiannual rate:**

   Since the interest is compounded semiannually, we divide the annual interest rate by 2:
   \[
   r = \frac{1.05\%}{2} = \frac{0.0105}{2} = 0.00525
   \]

2. **Determine the total number of periods:**

   Since there are 2 periods per year (semiannual compounding) and the time is 6 years:
   \[
   n = 6 \times 2 = 12 \text{ periods}
   \]

3. **Substitute values into the future value formula:**

   \[
   FV = 850 \times \frac{(1 + 0.00525)^{12} - 1}{0.00525}
   \]

Let me calculate that for you.The future value of the ordinary annuity is approximately **$10,499.74**.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How does changing the interest rate affect the future value of an annuity?
2. What is the difference between an ordinary annuity and an annuity due?
3. How is the present value of an annuity calculated?
4. What would happen if payments were made quarterly instead of semiannually?
5. How does increasing the number of years impact the future value of an annuity?

**Tip:** The more frequently interest is compounded, the higher the future value due to more frequent application of interest on accumulated payments.

Find the future value for the ordinary annuity with the given payment and interest rate. PMT = $850; 1.05% compounded semiannually for 6 years. The future value of the ordinary annuity is $

Calculate the future value of an ordinary annuity with payments of $850 at an interest rate of 1.05% compounded semiannually for 6 years. This problem involves understanding annuities, compound interest, and the time value of money. Suitable for students in Grades 11-12.

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