(12C Platinum) Successive Discounts
12-22-2018, 09:07 AM (This post was last modified: 12-22-2018 06:10 PM by Dieter.)
Post: #2
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: (12C Platinum) Successive Discounts
(12-22-2018 05:07 AM)Gamo Wrote:  The two discounts cannot be simply added together
(20% + 5% = 25%) is inapplicable.

You have to use the following formula:

X = Price
Y = Discount %
Z = Discount %

Selling Price = X - [Y + Z - (Y*Z / 100)] * X

That's a quite complicated way of calculating accumulated discounts.
Edit: and most important, it's wrong. The term within the square brackets is the total discount in percent, so there is a factor 100 missing.

Doing it with discount factors is easier and not limited to just two successive discounts. Simply calculate 1 – d/100 for each discount rate d and multiply these factors. For 5%, 10% and 15% this yields 0,95 · 0,90 · 0,85 = 0,72675. Multiply the original price by this and get the discounted price. Also 1 minus that factor is the total discount rate, i.e. 0,27325 or 27,325%.

The last program in this post uses this approach.

(12-22-2018 05:07 AM)Gamo Wrote:  The successive discount on a product in a store is giving as
5%, 10% and 15%. The store price of the product is $1000. Then calculate overall discount and selling price of the product. 1000 [R/S] display 1000.00 5 [R/S] display 5.00 10 [R/S] display briefly 14.50 then 855.00 Answer for Total Discount % of the first two discount is 14.5% and Selling Price is$855.00

RCL 3 [R/S] display 1000.00
RCL 1 [R/S] display 14.50
15 [R/S] display briefly 27.33 then 726.75

Waaaay too complicated. ;-)
You don't even need a program for this:

Enter original price [ENTER] [ENTER] [ENTER]

For each discount:
Enter discout rate [%] [–] and get the dicounted price

Finally press [Δ%] to see the total discount in percent.

Example:

1000 [ENTER] [ENTER] [ENTER]
5 [%] [–] => 950,00
10 [%] [–] => 855,00
15 [%] [–] => 726,75

[Δ%] => –27,33 total discount in %

After this you can press [%] to see the total discounted amount.
Another [+] returns to the discounted price.

[%]  => –273,25   (total discount in € or \$ or whatever)
[+]  =>   726,75   (the discounted price again)

Code:
01 STO 0 02 R/S 03 x=0? 04 GTO 08 05 % 06 - 07 GTO 02 08 R↓ 09 RCL 0 10 X<>Y 11 Δ%

It can even be done without any data registers:

Code:
01 ENTER 02 ENTER 03 R/S 04 X=0? 05 GTO 09 06 % 07 - 08 GTO 03 09 + 10 Δ%

As usual, reset the program with f [PRGM] first.

Enter initial price [R/S]

Enter as many discounts as you want, each followed by [R/S]
The discounted price is displayed

After the last discount enter 0 [R/S]
The total discount in percent is displayed

1000 [R/S] => 1000,00

5 [R/S] => 950,00 (price after first discount)
10 [R/S] => 855,00 (price after second discount)
15 [R/S] => 726,75 (price after third discount)

0 [R(S] => –27,33 (total discount is 27,33%)

Here is another version that also displays the intermediate discount percentages.

Code:
01 STO 0 02 1 03 STO 1 04 1 05 RCL 1 06 - 07 EEX 08 2 09 x 10 PSE 11 RCL 0 12 RCL 1 13 x 14 R/S 15 RCL 1 16 % 17 STO-1 18 GTO 04

Same example:

f [PRGM]

1000 [R/S] =>    "0,00" 1000,00
5 [R/S] =>   "5,00"   950,00
10 [R/S] => "14,50"   855,00
15 [R/S] => "27,33"   726,75

When a result is displayed you may press [X<>Y] to show the accumulated discount rate and the disounted price again.

[X<>Y]   27,33
[X<>Y] 726,75

Dieter

Note: this post has been edited several times to add more programs and some other ideas which I had after I posted the original message. ;-)
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 Messages In This Thread (12C Platinum) Successive Discounts - Gamo - 12-22-2018, 05:07 AM RE: (12C Platinum) Successive Discounts - Dieter - 12-22-2018 09:07 AM RE: (12C Platinum) Successive Discounts - Werner - 12-23-2018, 09:11 AM RE: (12C Platinum) Successive Discounts - Dieter - 12-23-2018, 09:33 AM RE: (12C Platinum) Successive Discounts - Gamo - 12-23-2018, 03:05 PM RE: (12C Platinum) Successive Discounts - SlideRule - 12-23-2018, 03:13 PM RE: (12C Platinum) Successive Discounts - Dieter - 12-23-2018, 06:16 PM RE: (12C Platinum) Successive Discounts - SlideRule - 12-23-2018, 07:45 PM RE: (12C Platinum) Successive Discounts - Gamo - 12-24-2018, 06:32 AM RE: (12C Platinum) Successive Discounts - Thomas Klemm - 12-24-2018, 11:25 AM RE: (12C Platinum) Successive Discounts - Albert Chan - 12-24-2018, 12:52 PM

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