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.**