Interest Rates) Well-known financial writer Andrew Tobias argues that he can earn 177 percent per year buying wine by the case. Specifically, he assumes that he will consume one $10 bottle of fine Bordeaux per week for the next twelve weeks. He can either pay $10 per week or buy a case of 12 bottles today. If he buys the case, he receives a 10 percent discount, and, by doing so, earns the 177 percent. Assume he buys the wine and consumes the first bottle today. Do you agree with his analysis? Do you see a problem with his numbers?

I disagree and his numbers are clearly wrong.

Explanation:

there are 52 weeks in a year, so the you should consume 52 bottles of wine per year. By the way, $10 per bottle doesn't buy any fine wine, but lets follow the question.

If you buy each wine individually, you will spend $10 x 52 = $520.

If you buy the wine by cases, you will spend $520 x 90% = $468

the difference is clearly not 177%, it only represents $52 or 10%.

Even if you decided to invest your savings per case of wine = $12 x $10 x 10% = $12

his total savings per year = $52 are spread over the year, so you could consider them an annuity of 4 $12 payments and 1 $4 payment. In order for this annuity to represent a 177% gain, which is equivalent to $468 x 177% = $828.36, the interest rate should be extremely high.

FV of an annuity due = payment x FV annuity due factor

$828.36 = $12 x FV annuity due factor

FV annuity due factor = $828.36 / $12 = 69.03

the % earned in 4.3 periods that results in 69.03 is close to 150% per every 12 weeks. This is not a reasonable interest rate.