In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1589. They start with $130. 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

In​ March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost ​$1589. They start with ​$130. 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?

GPT 3.5 · Answer

To determine if the family will have enough money for their trip, we need to calculate the total amount they will have saved by the end of August.

Starting amount: $130

March deposit: $130 + 25% = $130 + $32.50 = $162.50
April deposit: $162.50 + 25% = $162.50 + $40.63 = $203.13
May deposit: $203.13 + 25% = $203.13 + $50.78 = $253.91
June deposit: $253.91 + 25% = $253.91 + $63.48 = $317.39
July deposit: $317.39 + 25% = $317.39 + $79.35 = $396.74
August deposit: $396.74 + 25% = $396.74 + $99.18 = $495.92

Total amount saved by the end of August: $130 + $162.50 + $203.13 + $253.91 + $317.39 + $396.74 + $495.92 = $1959.59

The family will have saved $1959.59 by the end of August, which is more than the expected cost of their vacation ($1589). Therefore, they will have enough money for their trip.

Amount they need for the trip: $1959.59 - $1589 = $370.59.