Question

Melissa has a savings account. She deposited $1,000 into the account the first year. For each year after the first, she plans to deposit an amount that is 2 percent greater than the amount deposited the preceding year. If she makes no other deposits, the total amount of the deposited money in years is the sum Sn

of a geometric series of n terms.

The formula for Sn
can be expressed as (1000(1−rn)1−r)
.

Melissa will have deposited approximately how much by year 30?

Responses

A.$30,000


B.$35,729


C.$40,568


D.$87,453

Answer 1

Explanation:

The formula for Sn of a geometric series with first term a and common ratio r is:

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

In this case, the first term a is $1,000, the common ratio r is 1.02 (since she's depositing 2% more each year), and n is 30 (since we're looking for the amount deposited after 30 years).

Plugging in these values, we get:

Sn = 1000((1-1.02^30)/(1-1.02))

Sn ≈ $87,453

Therefore, the answer is D. $87,453.