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I am trying to construct an equation for calculating a price, that takes into account compound interest of 10%.

1 item  = $10
2 items = $19
3 items = $27.1

so for a given number of items, I can calculate the price.

pingu
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1 Answers1

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You are saying that the first item costs $10$, the second $10*0.9$, the third $10*0.9^2$. The total is then a geometric series: $10(1+0.9+0.9^2+\ldots 0.9^n)$ which sums to $10\left(\frac {1-0.9^{n}}{1-0.9}\right)$

Ross Millikan
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  • That's great! thanks very much Ross. Would it be difficult to adjust that equation so that the first term was $10 the second was ((100.8) 0.9), the third ((100.8)0.9^2). Essentially the base price is reduced by 20% for all terms but the first. – pingu Apr 25 '13 at 08:34
  • @pingu: Then consider the first item special. You just change the factor $10$ to $8$, but add 2 to fix the price of the first one. – Ross Millikan Apr 25 '13 at 13:04
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    and an infinite number costs a total of $100 – Henry Apr 26 '13 at 22:47
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    @Henry: Good point. I'll take 'em. How much is the shipping? – Ross Millikan Apr 26 '13 at 22:48
  • @Henry - That is actually what I wanted, the items in question are actually web service accounts, and I want the price to tend towards an upper limit. – pingu Apr 30 '13 at 20:15
  • @Ross - Not convinced the above equation is correct, when you have 1 item, it calculates the price as $19 – pingu Apr 30 '13 at 20:58
  • @pingu: sorry-off by one in the exponent – Ross Millikan Apr 30 '13 at 21:04
  • @Ross - If I try and correct it by changing the exponent from (n+1) to just (n) then i cant get it to work with my additional question of the first term being a special case. – pingu Apr 30 '13 at 21:04
  • @Ross - I have an additional problem. If I change the exponent to (n-1) so that the equation above evaluates to 0 for n=1, so that I am able to add the first term as a special case, then when n=2 the second item has no compound discount applied. – pingu Apr 30 '13 at 21:10
  • I have added my follow up question as a new question here http://math.stackexchange.com/questions/377624/geometric-series-to-calculate-price – pingu Apr 30 '13 at 21:36
  • @pingu: The exponent was $n+1$. I have changed it to $n$ which works perfectly. – Ross Millikan Apr 30 '13 at 22:19