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13 July, 06:16

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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  1. 13 July, 06:44
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    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
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