To calculate the future value of an ordinary annuity, we can use the formula:

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

where:

• $P$ is the payment per period ($125 in this case),
• $r$ is the monthly interest rate,
• $n$ is the total number of payments.

Step 1: Identify the Variables

• Monthly payment, $P = 125$
• Annual interest rate, $5.5\%$
• Time period, $12$ years
• Compounding period is monthly.

Step 2: Calculate Monthly Interest Rate

Since the interest rate is compounded monthly, convert the annual rate to a monthly rate: $r = \frac{5.5\%}{12} = \frac{0.055}{12} \approx 0.00458333$

Step 3: Calculate Total Number of Payments

Since there are 12 payments per year for 12 years: $n = 12 \times 12 = 144$

Step 4: Substitute Values into the Formula

$FV = 125 \times \frac{(1 + 0.00458333)^{144} - 1}{0.00458333}$

Step 5: Calculate the Future Value

Using the values above, let's calculate:

$FV \approx 125 \times \frac{(1.00458333)^{144} - 1}{0.00458333}$

1. Calculate $(1.00458333)^{144} \approx 1.9253382$.
2. Subtract 1: $1.9253382 - 1 = 0.9253382$.
3. Divide by $r$: $\frac{0.9253382}{0.00458333} \approx 201.99$.
4. Multiply by $P$: $125 \times 201.99 \approx 25248.75$.

Answer

The future value of the annuity is approximately:

$\boxed{25,248.75}$

Would you like further details on annuity calculations, or do you have any questions?

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Here are five additional questions to consider:

1. How does changing the compounding frequency impact the future value?
2. What would the future value be if payments were made at the beginning of each period (annuity due)?
3. How would the future value change with a higher interest rate?
4. How does extending the duration of payments affect the future value?
5. What is the difference in future value if the monthly deposit amount is doubled?

Tip: When calculating annuity values, rounding interest rates too early can lead to slightly inaccurate results.