Your grandmother has been putting $ 2 comma 000 into a savings account on every birthday since your first​ (that is, when you turned​ one). The account pays an interest rate of 7 %. How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday

To solve this problem, we can use the formula for the **future value of a series of cash flows (or annuity)**, since your grandmother makes a deposit every year and the account earns interest.

The formula for the future value $ FV $ of an annuity is:

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

Where:
- $ P $ is the annual deposit (in this case, $2,000),
- $ r $ is the annual interest rate (in this case, 7% or 0.07),
- $ n $ is the number of deposits (in this case, 18 since there are deposits starting from your first birthday through your 18th birthday).

### Step-by-Step Calculation:

1. **Annual deposit** $ P $ = $2,000.
2. **Annual interest rate** $ r $ = 7% = 0.07.
3. **Number of deposits** $ n $ = 18.

Let's calculate this.The amount of money in the account immediately after your grandmother makes the deposit on your 18th birthday will be approximately **$67,998.07**.

Would you like more details on any part of the calculation? Here are 5 related questions for further exploration:

1. What would the balance be if the interest rate were lower, say 5%?
2. How much interest has been earned by the 18th birthday?
3. How would the final amount change if the deposits were made at the end of each year instead?
4. What would be the future value if deposits were made for 25 years instead of 18?
5. How would monthly deposits of $200 instead of yearly deposits affect the total?

**Tip:** The earlier you start saving or investing, the more you benefit from compound interest over time.

Your grandmother has been putting $2,000 into a savings account on every birthday since your first (that is, when you turned one). The account pays an interest rate of 7%. How much money will be in the account immediately after your grandmother makes the deposit on your 18th birthday?

Calculate the future value of annual $2,000 deposits into a savings account with a 7% interest rate over 18 years. This problem explains the future value of an annuity formula and explores how compound interest grows your savings.

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