Financial
Reverse discount formula: find original price before a percentage discount
Divide SalePrice by (1 - DiscountPct) to recover exact list price—avoiding the common mistake of multiplying SalePrice by (1 + DiscountPct).
Why $68 after 15% off came from $80.00—not $78.20
Because a 15% discount subtracts 15% of the ORIGINAL ListPrice, SalePrice = ListPrice * (1 - 0.15) = ListPrice * 0.85.
Solving for ListPrice divides SalePrice by (1 - DiscPct): $68 / 0.85 = $80.00 ($80 * 15% = $12 off -> $68). Multiplying $68 * 1.15 computes 15% of the smaller discounted price and lands short at $78.20!
If the sale amount was rounded, several original prices can produce it; the rounded reverse result is an estimate under the stated percentage. The implied-discount formula requires a positive list price.
| SalePrice (A) | DiscPct (B) | Wrong A*(1+B) | Exact List A/(1-B) |
|---|---|---|---|
| 68 | 0.15 | 78.20 (wrong) | 80.00 |
| 150 | 0.25 | 187.50 (wrong) | 200.00 |
Reverse list-price, forward sale-price, and implied discount %
Require a discount from 0 inclusive to 1 exclusive and a nonnegative sale amount. At 100% the original price cannot be inferred, and greater discounts are outside this example’s domain.
=IF(OR(B2<0,B2>=1), "Cannot infer price", ROUND(A2 / (1 - B2), 2))Implied discount percentage from List and Sale
1 - (SalePrice / ListPrice) computes 1 - 68/80 = 0.15 (15% off).
=ROUND(1 - (A2 / C2), 4)Try the example
Use the original values or change them to test your understanding.