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:

$\boxed{69,936.65}$

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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.