Chapter 12.3, Problem 97AYU

To determine

To find: The total amount.

Answer to Problem 97AYU

The total amount paid off in 22 days will be $ 4,1943.03 pennies and the payment on 22^nd workday will be $ 20,971.52Option. The risk is that if I fall sick, there will be no pay and no increase in pay. If I do not have any better offer, I should accept this.

Explanation of Solution

Given information:

  $Day-wise-payment:\text{ 1, 2, 4,}\mathrm{............}\text{(22 days)}$

Calculation:

Calculate the value of $S_{22}$ .

Use formula: $S_n=\frac{a\left(r^n-1\right)}{r-1}$

  $\begin{array}{c}{S}_{22}=\frac{1\left({\left(2\right)}^{22}-1\right)}{2-1}\\ =4194303pennies\\ =\$41943.03\end{array}$

Calculate the value of $a_{22}$

Use formula: $a_n=a.r^{n-1}$

  $\begin{array}{c}{a}_{22}=a.r^{22-1}\\ $ =1{(2)}^{21}$=2097152pennies\\ =\$20971.52\end{array}$

Therefore, the total amount paid off in 22 days will be $ 4,1943.03 pennies and the payment on 22^nd workday will be $ 20,971.52Option. The risk is that if I fall sick, there will be no pay and no increase in pay. If I do not have any better offer, I should accept this.