Chapter 12.3, Problem 96AYU

To determine

To find: The option that provides the most money and the option that provides the least money and the option that should be chosen.

Answer to Problem 96AYU

The Option 1 provides the most money and Option 3 provides the least money and Option 1 should be chosen as it provides the most money.

Explanation of Solution

Given information:

  $\begin{array}{l}Option1:2000000,2100000,2200000,\dots \dots \dots \dots \dots \dots .\left(7terms\right)\\ Option2:2000000,2000000(1+\frac{4.5}{100}),2000000{(}^1\dots \dots \dots \dots \dots \left(\text{7 }terms\right)\\ Option3:2000000,2095000,219000,\mathrm{.............}(7terms)\end{array}$

Calculation:

Calculate the value of $S_7$ .

Use formula: $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$

  $\begin{array}{c}{S}_7=\frac{7}{2}\left[2(2000000)+(7-1)(100000)\right]\\ =16,8000,000\end{array}$

Calculate the value of $S_7^{/}$

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

  $\begin{array}{c}{S}_7^{/}=\frac{2000000\left({\left(\frac{209}{200}\right)}^7-1\right)}{\frac{209}{200}-1}\\ =16,038,303.58\end{array}$

Calculate the value of $S_7^{//}$ .

Use formula: $S_n=\frac{n}{2}\left[2a+(n-1)d\right]$

  $\begin{array}{c}{S}_7^{//}=\frac{7}{2}\left[2(2000000)+(7-1)(95000)\right]\\ =15,995,000\end{array}$

Therefore, Option 1 provides the most money and Option 3 provides the least money and Option 1 should be chosen as it provides the most money.