Your grandmother has been putting ​$800 into a savings account on every birthday since your first​ (that is, when you turned​ one). The account pays an interest rate of 9%. How much money will be in the account immediately after your grandmother makes the deposit on your 18th ​birthday?
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Part 1
The amount in the account upon your 18th birthday is ​$enter your response here.  ​(Round to the nearest​ cent.)

To solve this, we need to calculate the future value of the 18 deposits made by your grandmother into the savings account. Since these deposits are made annually, we can use the **future value of an annuity formula**:

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

Where:
- $ FV $ is the future value of the account.
- $ P = 800 $ is the annual deposit amount.
- $ r = 9\% = 0.09 $ is the annual interest rate.
- $ n = 18 $ is the number of years (deposits).

However, since each deposit earns interest over a different number of years, we need to calculate the future value for each individual deposit and sum them up. Specifically, the first deposit earns interest for 17 years, the second for 16 years, and so on, until the final deposit, which earns no interest.

We can calculate this step-by-step. Let me compute it for you.The amount in the account immediately after your grandmother makes the deposit on your 18th birthday is **$36,014.77**.

Would you like more details or have any questions?

Here are some related questions for deeper exploration:
1. How would the total change if the interest rate were 5% instead of 9%?
2. What if the deposits were made monthly instead of annually?
3. How much would be in the account after 25 years with no further deposits?
4. What if the initial deposit amount was $1,000 instead of $800?
5. How does the future value formula apply when interest is compounded quarterly?

**Tip**: The earlier you invest money, the more it can grow thanks to compound interest!

Your grandmother has been putting ​$800 into a savings account on every birthday since your first​ (that is, when you turned​ one). The account pays an interest rate of 9%. How much money will be in the account immediately after your grandmother makes the deposit on your 18th ​birthday?

Learn how to calculate the future value of an annuity when $800 is deposited annually for 18 years with a 9% interest rate. This problem covers key concepts in compound interest and future value calculations, using the formula for annuities. Suitable for high school students in Grades 10-12.

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