# You deposit $200 in a savings account.for each year thereafter , you plan to deposit 15% more than the previous year . About how much money will you have deposited in all after 20 years?

##### 1 Answer

#### Explanation:

Amounts the person in question deposits each year

#$ color(white)(l) 200# in the first#1"st"# year,#(1+15%) xx $ color(white)(l) 200# in the second#2"nd"# year,#(1+15%)^2 xx $ color(white)(l) 200# in the third#3"rd"# year,#cdot cdot cdot# #(1+15%)^19 xx $ color(white)(l) 200# in the twentieth#20"th"# year,

form a geometric sequence.

A general formula gives the sum of the first

The geometric sequence in this question has

as its common ratio and

as the first term, which equals to the deposit in the very first year.

The question is asking for the sum of the first twentieth terms of this sequence, implying

(rounded to the two decimal places)

Therefore the person would have deposited