Yesterday morning I was listening to WNYC/NPR during my commute. The reporter was explaining De Beers’ claim of supply shortage of diamonds and there will be a price increase of 5% a year for the next 5 years. In closing of the story, the reporter said something about the effect of price hike of 25%, thus implying that 5% annual increase over 5 years equals to 25% increase in total!
Let’s take a look at the concept of compound interest. First let’s say we start with the price of a mythical diamond at $100. At the end of first year, we increase price by 5%. That is $100 + ($100 x 5%) = $105.
So at the beginning of second year, the price of the mythical diamond is now at $105. At the end second year, we increase price by 5% again. This time $105 + ($105 x 5%) = $110.25.
Repeat this for the next three years:
Year 3: $110.25 + ($110.25 x 5%) = $115.76
Year 4: $115.76 + ($115.76 x 5%) = $121.55
Year 5: $121.55 + ($121.55 x 5%) = $127.63
So at the beginning of fifth year, the last price increase puts the final price of our mythical diamond at $127.63.
But what about the 25% increase in 5 years? Ok, let’s see.
$100 + ($100 x 25%) = $125
Huh! That’s clearly not the same as $127.63!
So my message to liberal arts graduates who may (or may not) become a reporter who would work on story involves numbers: brush up your maths skill!