Chapter 12.3, Problem 94AYU

To determine

To find: The offer which is better.

Answer to Problem 94AYU

The second offer is better.

Explanation of Solution

Given information:

Starting salary = $20000 and $ 22000.

Increase = 6% and 3%

Time= 5 years

Calculation:

Calculate the value of $a_6\text{and}{a^{\prime }}_6$ .

  $\begin{array}{c}{a}_6=a{\left(1+\frac{r}{100}\right)}^5\\ =20000{\left(\frac{106}{100}\right)}^5\\ =26,764.51\end{array}$

  $\begin{array}{c}{a}_6^{/}=a{\left(1+\frac{r}{100}\right)}^5\\ =22000{\left(\frac{103}{100}\right)}^5\\ =25,504.03\end{array}$

Therefore, after 5 years the salary in the first offer will be better.

Calculate the value of $S_5\text{and}{S}_5^{/}$ .

  $\begin{array}{c}{S}_5=\frac{a\left(r^5-1\right)}{r-1}\\ =\frac{20000\left({\left(\frac{106}{100}\right)}^5-1\right)}{\frac{106}{100}-1}\\ =112,741.86\end{array}$

  $\begin{array}{c}{S}_5^{/}=\frac{a\left(r^5-1\right)}{r-1}\\ =\frac{20000\left({\left(\frac{103}{100}\right)}^5-1\right)}{\frac{103}{100}-1}\\ =116,800.99\end{array}$

Therefore, the total income in 5 years will be greater in the second offer.