Round your answers to two decimal places, if necessary.
At the beginning of each of the last three years, Lucas put $7,000 from his earnings as a waiter into a college savings account that earned 1.7% interest compounded annually. Now he will spend an estimated $21,600 to attend his local community college for 2 years and not take out a student loan. Complete the table to determine whether Lucas has saved enough money to attend community college
The Correct Answer and Explanation is :
To solve this problem, we need to calculate the balance in Lucas’s savings account after three years, taking into account the annual deposit of $7,000 and the interest of 1.7% compounded annually.
Let’s break it down year by year:
Year 1:
- Beginning balance: $0 (since it is the start of the first year)
- Amount deposited: $7,000
- Interest earned: $7,000 × 1.7% = $119
- New balance: $7,000 + $119 = $7,119
- Ending balance: $7,119
Year 2:
- Beginning balance: $7,119
- Amount deposited: $7,000
- Interest earned: ($7,119 + $7,000) × 1.7% = $240.02
- New balance: $7,119 + $7,000 + $240.02 = $14,359.02
- Ending balance: $14,359.02
Year 3:
- Beginning balance: $14,359.02
- Amount deposited: $7,000
- Interest earned: ($14,359.02 + $7,000) × 1.7% = $361.10
- New balance: $14,359.02 + $7,000 + $361.10 = $21,720.12
- Ending balance: $21,720.12
Conclusion:
- Total balance at the end of Year 3: $21,720.12
- Amount Lucas needs for college: $21,600
- Does Lucas have enough money? Yes, Lucas has saved $21,720.12, which is enough to cover the $21,600 cost of attending community college.
Now, I’ll generate the table image for you based on these calculations.
Here is the table showing the calculations for Lucas’s savings account over three years, including the deposits, interest earned, and new balances each year. Based on this, Lucas has saved enough to attend community college, with a final balance of $21,720.12, which is more than the required $21,600.
Let me know if you’d like further clarification or any adjustments!
