Question

115. Sami opens an account and deposits $100 into it at the end of each month. The account earns 2% per year compounded monthly. Let Sn denote the amount of money in her account at the end of n months (just after she makes a deposit). For example, S1 = 100 and S2 = 100(1 + 0.02 /12)+100

a. Write a geometric series for the amount of money in the account after 3, 4, and 5 months.

Answer 1

Explanation:

Geometric series.

Month 3.

100(1+\frac{0.02}{12})^2 + 100(1+\frac{0.02}{12})+100

Month 4.

100( 1 + \frac{0.02}{12})^3 + 100( 1 + \frac{0.02}{12})^2+100(1+\frac{0.02}{12})+100

Month 5.

100(1 + \frac{0.02}{12})^4 + 100(1 + \frac{0.02}{12})^3 + 100(1 + \frac{0.02}{12})^2 +100( 1 + \frac{0.02}{12}) + 100