Question

(a) worked out incorrectly; or (b) worked out correctly but using a method not specified in the problem statement; or (c) not solved completely, but the answer is stated with inadequate or no work shown, EVEN IF THE FINAL ANSWER IS CORRECT.

Answer 1

As per the question, the compensation for the first year will be $36000

The compensation for the second year will be 5% more, that is $36000+5\%(36000)=36000(1+5\%)=36000(1+0.05)=36000(1.05)=37800$

Similarly, the compensation for the 3rd year will be

$37800+5\%(37800)=36000(1.05)+5\%(36000*1.05)=36000*1.05(1+5\%)=36000*(1.05)^2$

.Therefore, we can write the compensation for the nth year as

36000 + (1.05)-

The total compensation across n years, will therefore be

$36000+(36000*1.05)+(36000*1.05^2)+........+36000*1.05^{n-1}$

As we can see, this is a geometric sum

The value of a geometric sum can be given by the formula

$S_n=a(1-r^n)/(1-r)$, where S is the sum, a the initial term, and r the common difference.

We need to find the compensation across 20 years, so $n=20$

Therefore, we can write the sum as

$S_{20}=36000(1-1.05^{20})/(1-1.05)$

$S_{20}=36000(1-2.6533)/(1-1.05)$

$S_{20}=36000(1.6533)/(0.05)$

$S_{20}=36000*33.066$

Hence, the total compensation across 20 years will be 1190376 dollars