Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if ​$70 is invested semiannually for 30 years at 6.5​% compounded semiannually.

The formula for the future value of an ordinary annuity is:

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

Where:
- $ A $ is the accumulated amount in the annuity.
- $ P $ is the periodic payment.
- $ r $ is the interest rate per period.
- $ n $ is the total number of periods.

### Given values:
- $ P = 70 $ (the amount invested semiannually)
- $ 6.5\% $ annual interest rate, so the semiannual rate is $ r = \frac{6.5\%}{2} = 3.25\% = 0.0325 $
- The investment is for 30 years, and since payments are made semiannually, the number of periods is $ n = 30 \times 2 = 60 $

Now, let's plug the values into the formula and calculate the accumulated amount.

\[
A = 70 \times \frac{(1 + 0.0325)^{60} - 1}{0.0325}
\]

I'll calculate this step by step for you.The accumulated amount in the annuity after 30 years, with $70 invested semiannually at 6.5% compounded semiannually, is approximately **$12,522.51**.

Would you like further details on how the calculation was done, or do you have any other questions?

Here are five related questions:
1. How does changing the interest rate affect the accumulated amount in an annuity?
2. What happens if payments are made monthly instead of semiannually?
3. Can this formula be used for other investment strategies?
4. How does compound interest compare to simple interest in annuities?
5. What is the difference between an ordinary annuity and an annuity due?

**Tip**: The longer you invest in an annuity with compound interest, the greater the effect of compounding over time!

Discover how to calculate the accumulated amount of an ordinary annuity where $70 is invested semiannually at 6.5% interest for 30 years. Learn key concepts such as the future value formula for annuities, compound interest, and the time value of money.

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