Brain Teasers
Mad Ade's Cousin's Raise
In the legendary land of Madadia, everything is wonderful. There is no inflation, so Madadian wonks (local currency 100 winks = 1 wonk) are constant in value.
Mad Ade's cousin Manic Martin works as an accountant in one of Madadia's leading accounting firms.
After his first year his salary was a straight 10,000 wonks, with which Manic Martin was quite happy. His manager was so impressed with his work he offered Manic Martin a wage rise.
Now this being Madadia, things are not always done as they are elsewhere, the wage rise was offered over a 17.5 year contract period, These contracts are immutably binding, and will still be paid to benefactors in the event of death or permanent disability.
Manic Martin has a choice of how to receive his raise. The first option was for an immediate 5% raise to 10,500 wonks annually, with an additional 5% raise every 6 months. The second option was for an immediate 10% raise to 11,000 wonks annually, with an additional 10% raise every year. Manic Martin's salary, based upon his current annual, was paid bi-weekly.
Which deal would benefit Manic Martin the most?
Mad Ade's cousin Manic Martin works as an accountant in one of Madadia's leading accounting firms.
After his first year his salary was a straight 10,000 wonks, with which Manic Martin was quite happy. His manager was so impressed with his work he offered Manic Martin a wage rise.
Now this being Madadia, things are not always done as they are elsewhere, the wage rise was offered over a 17.5 year contract period, These contracts are immutably binding, and will still be paid to benefactors in the event of death or permanent disability.
Manic Martin has a choice of how to receive his raise. The first option was for an immediate 5% raise to 10,500 wonks annually, with an additional 5% raise every 6 months. The second option was for an immediate 10% raise to 11,000 wonks annually, with an additional 10% raise every year. Manic Martin's salary, based upon his current annual, was paid bi-weekly.
Which deal would benefit Manic Martin the most?
Answer
The 5% semi-annual raise yields a higher return.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.
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