Question

Look at the expression you entered in the table in part C. Write them backward as a sum, starting with the amount from month 12. You should recognize a geometric series. Use the formula for the sum of a geometric series to determine the amount of money is Esther’s savings account at the end of 1 year after depositing $50 each month. How much money did she earn from interest.

Answer 1

Per month Additions Interest Balance

Start $0.00 $0.00

1 $50.00 $0.15 $50.15

2 $50.00 $0.30 $100.45

3 $50.00 $0.45 $150.90

4 $50.00 $0.60 $201.50

5 $50.00 $0.75 $252.25

6 $50.00 $0.91 $303.16

7 $50.00 $1.06 $354.22

8 $50.00 $1.21 $405.43

9 $50.00 $1.37 $456.80

10 $50.00 $1.52 $508.32

11 $50.00 $1.67 $559.99

12 $50.00 $1.83 $611.82

Answer 2

Answer: =

Write the expressions backward from month 12 to month 1 to get this series:

50 + 50(1.003) + 50(1.003)2 + ... + 50(1.003)11

Convert the series to sigma notation, and find the sum of the 12 terms in the series:

11

S12 50(1.003)

ko

50(1 - 1.00312)

1 - 1.003

610

Esther will have about $610 in her savings account after a year. She would have deposited $600 over 12 months, so she

will have earned $10 in interest.

Explanation: