To determine the future value of the annuity that William will accumulate, we can use the future value of an annuity formula:

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

Where:

• $FV$ is the future value of the annuity.
• $P$ is the monthly payment.
• $r$ is the monthly interest rate.
• $n$ is the total number of payments.

Step 1: Determine the monthly payment, $P$

William buys 17 coffees per month at $2.50 each, so his monthly investment will be:

$P = 17 \times 2.50 = 42.50 \text{ dollars}$

Step 2: Determine the monthly interest rate, $r$

The annual interest rate is 4.8%, compounded monthly. Therefore, the monthly interest rate is:

r = \frac{4.8\%}{12} = \frac{0.048}{12} = 0.004 \text{ (or 0.4% per month)}

Step 3: Determine the total number of payments, $n$

William plans to invest for 25 years. Since payments are made monthly:

$n = 25 \times 12 = 300 \text{ payments}$

Step 4: Calculate the future value, $FV$

Now, substitute the values into the formula:

$FV = 42.50 \times \frac{(1 + 0.004)^{300} - 1}{0.004}$

Let's calculate this.

$FV = 42.50 \times \frac{(1.004)^{300} - 1}{0.004}$

$FV = 42.50 \times \frac{3.2434 - 1}{0.004}$

$FV = 42.50 \times \frac{2.2434}{0.004}$

$FV = 42.50 \times 560.85 = 23856.125 \text{ dollars}$

Final Answer:

The future value of the annuity will be approximately $23,856.13.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What would be the future value if the interest rate was 6% instead of 4.8%?
2. How would the future value change if William invested the money for 30 years instead of 25 years?
3. What would the future value be if William invested only $30 per month?
4. How much interest would William earn over the 25 years?
5. What would the future value be if the interest was compounded quarterly instead of monthly?

Tip: Always double-check the compounding period when calculating interest, as it can significantly affect the future value.