Question

In​ March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost ​$1362. They start with ​$125. At the beginning of each month they plan to deposit 20​% more than the previous month. Will they have enough money for their​ trip? If​ not, how much more do they​ need?Question content area bottomPart 1Select the correct answer below​ and, if​ necessary, fill in the answer box within your choice.A.​No, they need ​$enter your response here more. ​(Round up to the nearest​ dollar.)

Answer 1

To determine if the family will have enough money for their vacation by the end of August, we first need to calculate their monthly deposits.

1. Initial amount: $125
2. Desired vacation cost: $1362
3. Monthly increase of deposits: 20% more than the previous month

Monthly Deposits Calculation

• Month 1 (March): Deposit = $125
• Month 2 (April): Deposit = $125 + (20% of $125) = $125 + $25 = $150
• Month 3 (May): Deposit = $150 + (20% of $150) = $150 + $30 = $180
• Month 4 (June): Deposit = $180 + (20% of $180) = $180 + $36 = $216
• Month 5 (July): Deposit = $216 + (20% of $216) = $216 + $43.20 = $259.20 (rounded to $259)
• Month 6 (August): Deposit = $259 + (20% of $259) = $259 + $51.80 = $310.80 (rounded to $311)

Total Savings Calculation

Now, let's sum up the total savings by the end of August:

• March: $125
• April: $150
• May: $180
• June: $216
• July: $259
• August: $311

Total Amount Saved:

\[ Total\ Savings = 125 + 150 + 180 + 216 + 259 + 311 = 1241 \]

Determine if They Have Enough:

Now, we compare the total savings with the vacation cost:

• Total Saved: $1241
• Vacation Cost: $1362

Difference:

\[ Difference = Vacation Cost - Total Saved = 1362 - 1241 = 121 \]

Therefore, the family does not have enough money for their trip.

Conclusion:

A. No, they need $121 more.