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This question describes a recurring deposit annuity problem, where a father deposits $1200 annually, starting on the day his daughter was born, with the last deposit made on her 21st birthday. The account earns 4.75% interest compounded annually.

To solve the problem, we will use the formula for the future value of an ordinary annuity:

\[
A = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $A$ is the amount in the account at the end of the 21st year.
- $P = 1200$ is the annual deposit.
- $r = \frac{4.75}{100} = 0.0475$ is the annual interest rate.
- $n = 21$ is the number of years of deposits.

Let’s calculate step-by-step.

1. **Substitute the values:**
   \[
   A = 1200 \times \frac{(1 + 0.0475)^{21} - 1}{0.0475}
   \]
2. **Calculate the growth factor**:
   \[
   (1 + 0.0475)^{21} \approx 2.6835
   \]
3. **Find the future value factor**:
   \[
   \frac{2.6835 - 1}{0.0475} \approx 35.4453
   \]
4. **Calculate the final amount in the account**:
   \[
   A \approx 1200 \times 35.4453 = 42,534.36
   \]

Thus, the account will have approximately **$42,534.36** on the day of her 21st birthday.

Would you like further details on how the interest earned is calculated or any clarifications?

Here are some additional questions that expand on this:

1. How would the amount change if the interest rate was compounded monthly instead of annually?
2. What would be the total interest earned over the 21 years?
3. How does increasing the annual deposit affect the final amount?
4. What happens if the interest rate is lower, say 3%?
5. Can you derive the total amount for a different number of years, e.g., 25 years?

**Tip**: Always double-check your annuity formula inputs, especially when dealing with compounded interest.

A father opened a savings account for his daughter on the day she was born, depositing $1200. Each year on her birthday, he deposits another $1200, making the last deposit on her 21st birthday. If the account pays 4.75% interest compounded annually, how much is in the account at the end of the day on his daughter’s 21st birthday? How much interest has been earned?

This problem explores how to calculate the future value of a savings account with annual deposits of $1200, compounded at 4.75% interest annually. Suitable for high school students, this solution demonstrates step-by-step calculations for determining the total savings over 21 years.

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