To calculate the future value of the annuity, we use the future value formula for an ordinary annuity (payments made at the end of each period):

$FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}$

Where:

• $FV$ = future value of the annuity
• $P$ = quarterly payment
• $r$ = annual interest rate (as a decimal)
• $n$ = number of times the interest is compounded per year
• $t$ = number of years

Given the information:

• $P = 189$ (quarterly payment)
• $r = 0.05$ (5% annual interest rate)
• $n = 4$ (since interest is compounded quarterly)
• $t = 16$ years

Now, plug the values into the formula:

$FV = 189 \times \frac{(1 + 0.05/4)^{4 \times 16} - 1}{0.05/4}$

Let's calculate it step by step.

1. Interest rate per quarter:
   $\frac{0.05}{4} = 0.0125$

2. Total number of periods (quarters in 16 years):
   $4 \times 16 = 64 \text{ quarters}$

3. Compound factor:
   $(1 + 0.0125)^{64} = (1.0125)^{64} \approx 2.219640$

4. Subtract 1:
   $2.219640 - 1 = 1.219640$

5. Denominator (interest rate per quarter):
   $\frac{0.05}{4} = 0.0125$

6. Now calculate the future value:
   $FV = 189 \times \frac{1.219640}{0.0125} = 189 \times 97.5712 \approx 18434.53$

Thus, the total value of the annuity after 16 years is approximately $18,434.53.

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Would you like more details or explanations about any of the steps?

Here are 5 related questions:

1. How do I calculate the present value of an annuity?
2. What is the difference between ordinary annuities and annuities due (where payments are made at the beginning of the period)?
3. How would the future value change if the interest rate were higher or lower?
4. How does the number of compounding periods (quarterly, monthly, etc.) affect the future value of an annuity?
5. What would be the future value if the investment were made for a longer period or shorter period?

Tip: When dealing with compounded interest, it's important to adjust the interest rate and the number of periods according to the compounding frequency (quarterly, monthly, etc.).