Chapter 14, Problem 23T

Suppose a student smokes one pack of cigarettes per day at a cost of $3.00 per pack.

a. If the student quits smoking and puts the $3.00 saved per day in a jar, how much money will the student have saved at the end of 1 yr?

b. If the student takes the first year's savings from part (a) and invests the money in a bond fund paying 6% annual interest, how much will this money be worth 1 yr later?

c. Suppose that the student reinvests the principal and interest each year so that the money is compounded annually. The student will have:

End of year 1: $1095

End of year 2: $\left(1095\right)\left(1.06\right)=\$1160.70$

End of year 3: $\left(1095\right){\left(1.06\right)}^2=\$1230.34$

The sequence $a_n=\$1095{\left(1.06\right)}^{n-1}$ represents the value of the investment at the end of n years. Find the value of the investment after 30 yr. (Round to two decimal places.)

d. Now suppose that the student saves $1095 per year each year for 30 yr. Further suppose that the student invests each year's saving at 6% interest compounded annually. The following series represents the total savings plus interest over 30 yr. Find the sum.

${\displaystyle \underset{n=1}{\overset{30}{\sum }}1095{\left(1.06\right)}^{n-1}}$