Chapter 14, Problem 23T

(a)

To determine

To calculate: The amount of money saved by the student at the end of 1 year if the student quits smoking and puts the $\$5.50$ saved per day in a jar.

(b)

To determine

To calculate: The amount of money student would get if he invests the saved amount $\$2007.5$ from part (a) in a bond fund at $4\%$ annual interest.

(c)

To determine

To calculate: The value of investment after 30 years when student reinvests the principal and interest each year so that money is annually compounded and he has the following amount shown below,

End of year 1: $\$2007.50$.

End of year 2: $\left(\$2007.50\right)\left(1.04\right)=\$2087.80$

End of year 3: $\left(\$2007.50\right){\left(1.04\right)}^2=\$2171.31$

And the sequence $a_n=\$2007.50{\left(1.04\right)}^{n-1}$ represents the value of investment at the end of n years.

(d)

To determine

To calculate: The sum of geometric sequence ${\displaystyle \sum _{n=1}^{30}2007.5{\left(1.04\right)}^{n-1}}$ when the student saves $\$2007.50$ per year for 30 year at $4\%$

interest compounded annually.