In​ March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost ​$1484. They start with ​$120. At the beginning of each month they plan to deposit 25​% more than the previous month. Will they have enough money for their​ trip? If​ not, how much more do they​ need?

Question

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Part 1
Select 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.)
B.
​Yes, they will have enough money.

Answer 1

To determine if the family will have enough money for their vacation, we can calculate how much they will save from March to August.

1. Initial amount: $120

2. Cost of vacation: $1484

3. Months saving: The vacation is planned for the end of August, starting in March, results in six months of saving (March, April, May, June, July, August).

4. Depositing amount each month:

   • Month 1 (March): Starting deposit = $120
   • Month 2 (April): Deposit = $120 * 1.25 = $150
   • Month 3 (May): Deposit = $150 * 1.25 = $187.50
   • Month 4 (June): Deposit = $187.50 * 1.25 = $234.38 (rounding may be applied later)
   • Month 5 (July): Deposit = $234.38 * 1.25 = $292.98
   • Month 6 (August): Deposit = $292.98 * 1.25 ≈ $366.23 (again, rounding may apply)

5. Total deposits over six months:

• March: $120
• April: $150
• May: $187.50
• June: $234.38
• July: $292.98
• August: $366.23

Now, sum these amounts: \[ Total = 120 + 150 + 187.50 + 234.38 + 292.98 + 366.23 = 1351.09 \]

6. Total savings before the vacation: \[ Total Savings = Initial Amount + Total Deposited \] \[ Total Savings = 120 + 1351.09 = 1471.09 \]

7. Comparison with the vacation cost: \[ 1471.09 < 1484 \]

8. Calculate the shortfall: \[ 1484 - 1471.09 = 12.91 \]

Since we need to round up to the nearest dollar, they will need an additional $13.

Final Answer: A. No, they need $13 more.

Answer 2

round to the nearest dollar

Answer 3

Considering the previous calculation, we found that the family is short by $12.91. When rounding to the nearest dollar:

\[ 12.91 \text{ rounds to } 13. \]

Thus, the final answer remains the same:

A. No, they need $13 more.