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I am having a really hard time grasping how to effectively calculate "nested" percentages and the actual amount I save on each iteration

Example:

  • I purchase a gift card (Gift Card A) that has a \$200.00 value for a cost of $194.00 (3% discount)

  • Using Gift Card A value, I purchase Gift Card B that has a value of \$200.00 at the cost of $180.00 (10% discount)

  • Using Gift Card B value, I purchase Gift Card C that has a value of \$200.00 at a cost of $190.00 (5% discount)

  • Finally, using Gift Card C value, I purchase Gift Card D that has a value of \$100.00 at a cost of $90.00 (10% discount)

My first instinct would be that I saved a total of 28%, but I know it is not the case. If I use 0.97 * 0.9 * 0.95 * 0.9, I get 0.746415, which would be 25.36%. I am not sure if that is the correct answer and also do not know how I got there.

Also, I am unable to figure out how to calculate the actual amount I saved on each steps.

Thanks for any help!

ogmios
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  • exactly how are these percentages "nested"? It seems as if each purchased gift card are independent of one another, since you write that the discount is based from the value of the current gift card, not from the previous gift card. – Varun Iyer Dec 31 '15 at 00:48
  • If I use Gift Card A to purchase Gift Card B, then use Gift Card B to purchase Gift Card C and finally use Gift Card C to purchase Gift Card D, then I am certainly carrying discount% down the line, as it each time, I am getting a discount from previous card. Each card has its own discount, but it has additional discount from previous card discount...? – ogmios Dec 31 '15 at 07:53

1 Answers1

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Well, how much money did you spend? 194 dollars.

How much purchasing power do you have: 20 on card A, 10 dollars on card B, 110 dollars on card C. And 100 dollars on card D. 240 total.

You have \$240 purchasing power for \$194. A saving of \$46 or 46/240 = 19 1/6% savings.

fleablood
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  • Hmmph, thought I fixed that. – fleablood Dec 31 '15 at 00:58
  • You have now. :-) – Brian Tung Dec 31 '15 at 01:08
  • Not following this at all... :-( My purchasing power is really $200.00 on Card A. On Card B, it is still $200 because the value of B is $200. I use Card A to pay for card B, so I would only use $180 of the amount from Card A (Value is $200 for card A). So, if I use only $180 from Card A to pay for card B, I have $20 not used from Card A and the $180 used were only costing me $174.60 ($180 minus 3%). – ogmios Dec 31 '15 at 08:07
  • I do like your thinking about "how much did you spend? 194 dollars". It is true that the starting cost is total I do spend, but each time I buy a gift card with another gift card, I have a discount associated with new card% which reduce the cost of subsequent cards. Thus I do not use full balance each time and I have dollars unused from 1 card to the other. Technically, I am not getting that money back, but it is also money not used in the transactions, so equivalent to savings. – ogmios Dec 31 '15 at 08:13