In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1370. They start with $125 at the start 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

Mathematics

Leia Ballard

2 May, 17:27

In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1370. They start with $125 at the start 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?

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Answers (1)

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Elaina Jensen · Answer 1

Step-by-step explanation:

The savings for each month is increasing by 20%. It means that it is increasing in geometric progression. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1) / (r - 1)

Where

n represents the number of terms (months) in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

a = $125

r = 1 + 20/100 = 1.2

From March to August, it is 5 months. Thus,

n = 5 months

Therefore, the sum of the first 8

5 terms (months), S5 is

S5 = (125 * 1.2^ (5) - 1) / 1.2 - 1

S5 = (125 * 1.48832) / 0.2

S5 = 186.04/0.2

S5 = $930.2

They won't have enough money for the trip.

The additional amount of money that they need is

1370 - 930.2 = $439.8