Question

Help!

Suppose you are saving your money to pay for a vacation for your family. So far, you have $400 saved. You plan on saving more each month so you can pay for the vacation at the end of the year. Assume that you save 10% more each month than the previous month.

Answer 1

The sequence can be written as

month Amt. deposited

1 400

2 400 + 0.1x400

3 400 + 0.1x400 + 0.1(400 + 0.1x400) etc.

This can be generalized to 400(1 + 0.1)n-1 = 400 x 1.1n-1 amount deposited in the nth month.

This is a geometric sequence for which the sum is

(A). 400 (1 - 1.1n) / (1 - 1.1) = 8553.71 which is the total saved after 12 months (n).

(B). absolutely

(C). Much more than $8000 was saved.

I have a feeling there is some information missing as it is obvious that there will be more than enough after only 2 months! If the first month's deposit was not $400, the formula would still hold except that the initial amount would be substituted for $400.