John and Margaret deposit into a savings account for their son on his first birthday. They continue to make a deposit of on the child’s birthday, with the last deposit being made on the child’s 21 st birthday. If the account pays annual interest, which equation represents the amount of money in the account after the last deposit is made?

4. 
   Option 1
   Option 2
   Option 3
   Option 4

To solve this problem, let’s first understand how the deposits will grow over time. Each deposit made earns interest for a different number of years. The first deposit of $500 will accumulate interest for 21 years, the second deposit for 20 years, and so on, until the last deposit earns interest for just 1 year. Therefore, the total amount in the account after the last deposit can be represented as the sum of the future value of each deposit.

The correct equation combining all these components would look like:

This sequence can be represented using a geometric series formula, resulting in the equation:

Therefore, the correct answer here is Option 2, which shows the use of the formula for the sum of a geometric series.

Now consider a fun fact: when you put your money into a savings account with interest, you’re essentially making your money work for you! It’s like hiring your money to do a job — and just like a good employee, it keeps growing over time.

Speaking of personal finance, it’s also essential to understand the impact of starting to save early. Even small amounts can turn into a large nest egg due to compound interest over time. Imagine if instead of the first birthday, you had started saving on the day they were born!