This problem involves finding the future value of an annuity with annual deposits, but with the first deposit being made immediately. This type of problem can be solved using the future value of an annuity due formula:

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

Where:

• $FV$ is the future value of the annuity.
• $P$ is the annual deposit ($1,410.00).
• $r$ is the annual interest rate (11% or 0.11).
• $n$ is the number of years (17 years).

Step 1: Plug in the values:

• $P = 1410$
• $r = 0.11$
• $n = 17$

$FV = 1410 \times \frac{(1 + 0.11)^{17} - 1}{0.11} \times (1 + 0.11)$

Step 2: Calculate:

1. First, calculate $(1 + 0.11)^{17}$:

$(1 + 0.11)^{17} \approx 5.506$

2. Then subtract 1:

$5.506 - 1 = 4.506$

3. Now divide by the interest rate $r = 0.11$:

$\frac{4.506}{0.11} \approx 40.055$

4. Multiply by $P = 1410$:

$1410 \times 40.055 \approx 56,501.55$

5. Finally, multiply by $(1 + 0.11) = 1.11$:

$56,501.55 \times 1.11 \approx 62,766.72$

Final Answer:

The total amount in the account after 17 years will be approximately $62,766.72.

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Would you like more details on any part of this calculation? Or do you have any follow-up questions?

Related Questions:

1. What is the future value if the deposit is made at the end of each year (ordinary annuity)?
2. How would the result change if the interest rate were 9% instead of 11%?
3. If Derek started depositing $1,410 for 10 years instead of 17, what would the future value be?
4. How does the frequency of deposits (e.g., monthly or quarterly) affect the future value of an account?
5. What are the advantages and disadvantages of making deposits at the beginning of each period (annuity due) versus at the end (ordinary annuity)?

Tip:

When calculating future value of annuities, always ensure to use the correct formula based on whether the deposit is made at the beginning (annuity due) or the end (ordinary annuity) of each period!