The Accountant

This may have been your first guess, but there is something odd about the answer. At the start of the problem, the 10% raise is earning more- $11,000 annually vs. $10,500. After the first year, the 5% option has earned $10,762 compared to $11,000.

What are the two options earning at the moment the contract closes, after 17.5 years? Surprisingly, the 5% option only realizes a little more than $55,160, compared to the 10% option which is still ahead with just under 56,000.

So where's the advantage in the 5% option? It hides in the second half of every year. Even in the first year, the 5% option makes more in the second six months than the 10% option. For the first few years, this is not enough to offset the difference. But cumulatively, over seventeen and a half years, 5% realizes a grand total of $390.27 more than the 10% option. This in spite of the fact that the 10% option starts with a higher salary- and finishes with a higher salary.