## Friday, February 20, 2009

### BRAINTENANCE QUIZ 2/19/09

Dear Friends:

Firstly, the answer to yesterday's puzzle:

1. Given the same circumstances above, and the same rate of confusion as above, if a similar (and equally ambitious but careless) young man starts off with 100 young ladies, and makes this mistake 4 years in succession, and assuming that he does not add any new ladies to his portfolio, or win any deceived and hurt young ladies back, despite his charms and creative excuses, how many young ladies will remain available to him at the end of four fateful Valentine's Day debacles?

The young man will lose 20 young ladies after the first Valentine's Day (20% attrition due to his carelessness); of the remaining 80, he will lose 16 after the second Valentine's Day; of the remaining 64, he will lose 12.8 (let's round that last partial young lady up to a whole person, and say 13) after the third Valentine's Day; of the remaining 51, he will lose 10.2 (let's round that last partial young lady down to the next whole young lady, and say 10) after the fourth Valentine's Day, bringing his group of young female admirers down to 41.
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Here are several questions concerning simple interest, compound interest and accumulation of funds. It today's economy, these are practical questions. In each case, assume we invest the principal sum of \$100,000.00 at the beginning.

1) If interest accumulates at 10% per year simple, how much will the investment be worth at the end of ten years?

2) If interest accumulates at 7.5% per year compounded annually, how much will the investment be worth at the end of ten years?

3) If interest accumulates at 7.5% per year compounded annually, and the investor (my Uncle Phil) takes \$5,000 out of the account at the end of each year, how much will be in the investment account at the end of ten years?

Faithfully,

Douglas Castle
p.s. Please take the weekend to work on this one. We'll have our answers on Monday.