To find the future value (FV) of an ordinary annuity (where deposits are made at the end of each period), we use the formula:

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

Where:

• $P$ is the deposit amount ($200),
• $r$ is the interest rate per period,
• $n$ is the total number of periods.

Step 1: Identify values

• Monthly deposit ($P$): $200
• Annual interest rate: 7%, or 0.07 as a decimal.
• Compounding periods per year: 12 (monthly).
• Number of years: 15.

Step 2: Calculate values needed for the formula

1. Interest rate per period ($r$): $r = \frac{0.07}{12} = 0.0058333$

2. Total number of periods ($n$): $n = 15 \times 12 = 180$

Step 3: Apply the formula

Now we can substitute the values into the future value formula:

$FV = 200 \times \left( \frac{(1 + 0.0058333)^{180} - 1}{0.0058333} \right)$

Step 4: Solve

First, calculate $(1 + 0.0058333)^{180}$: $(1.0058333)^{180} \approx 2.8497$ Now apply the rest of the formula: $FV = 200 \times \left( \frac{2.8497 - 1}{0.0058333} \right)$ $FV = 200 \times \left( \frac{1.8497}{0.0058333} \right)$ $FV = 200 \times 316.989 \approx 63,398$

Final Answer:

The future value of the annuity is approximately $63,400.

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Would you like more details on how the formula was applied or help with a similar question?

Here are five related questions:

1. How would the future value change if the interest rate was 5% instead of 7%?
2. What would the future value be if deposits were made quarterly instead of monthly?
3. How do you calculate the present value of an annuity?
4. How does compound interest affect annuities compared to simple interest?
5. What if the deposits were made at the beginning of each period (annuity due)?

Tip: Increasing the frequency of compounding generally leads to a higher future value, as interest is applied more often.