(12C Platinum) Successive Discounts

[Dieter]

(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

To add the third discount.

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)

If you really want to use a program, what about this one (RPN mode):

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

Your example:

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. ;-)