Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity.
​$500 invested quarterly for 20 years at a 4.5​% interest rate compounded quarterly

To determine the **accumulated amount in an ordinary annuity**, we use the following formula:

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

where:
- $A$ = Accumulated amount  
- $P$ = Payment amount per period = 500  
- $r$ = Interest rate per period = $\frac{4.5\%}{4} = \frac{0.045}{4} = 0.01125$  
- $n$ = Total number of payments = $4 \times 20 = 80$  
- Compounded quarterly

### Step-by-Step Calculation:

1. **Calculate** $1 + r$:
   \[
   1 + r = 1 + 0.01125 = 1.01125
   \]

2. **Raise** $1.01125$ to the power of 80:
   \[
   1.01125^{80} \approx 2.5687
   \]

3. **Subtract 1** from the result:
   \[
   2.5687 - 1 = 1.5687
   \]

4. **Divide by r** (0.01125):
   \[
   \frac{1.5687}{0.01125} \approx 139.8733
   \]

5. **Multiply** by $P = 500$:
   \[
   500 \times 139.8733 \approx 69,936.65
   \]

### Final Answer:
The accumulated amount in the annuity after 20 years is approximately:

\[
\boxed{69,936.65}
\]

---

Do you have any questions, or would you like further clarifications?  
Here are 5 related questions you might find useful:

1. What is the difference between ordinary annuities and annuities due?  
2. How does compounding frequency affect the final amount?  
3. How would the result change if the interest rate were 6% instead of 4.5%?  
4. What if the payments were made monthly instead of quarterly?  
5. How can I calculate the present value of this annuity?  

**Tip:** Increasing the compounding frequency (e.g., monthly or daily) slightly increases the accumulated amount since interest is applied more often.

Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity. $500 invested quarterly for 20 years at a 4.5% interest rate compounded quarterly.

Learn how to calculate the accumulated amount for an ordinary annuity with a $500 quarterly investment, 4.5% annual interest rate compounded quarterly, and a 20-year period. This problem covers key financial concepts like annuities and compound interest, suitable for Grades 10-12.

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