Discount
A discount is a reduction in price, usually expressed as a percentage of the original price.
Formula
\text{discount amount} = \text{original price} \times \text{discount rate}; \quad \text{sale price} = \text{original price} \times (1 - \text{discount rate})
Definition
A discount is an amount taken off the original price: a $20\%$ discount means you pay $20\%$ less, found by multiplying the original price by the discount percent. Formally, discount $D = Pd$ (where $d$ is the discount rate as a decimal) and sale price $S = P - D = P(1 - d)$; sequential discounts do not simply add, a $20\%$ discount followed by a $10\%$ discount gives a combined multiplier of $0.8 \times 0.9 = 0.72$, a total $28\%$ discount, not $30\%$. A sequence of $n$ discounts $d_1, d_2, \ldots, d_n$ yields a combined multiplier of $\prod (1-d_i)$, the same mathematical structure used in present-value analysis, where $PV = FV/(1+r)^t$ discounts future cash flows back to their present equivalent, the "time value of money."
Example
A $\$60$ sweater that is $25\%$ off has a discount of $\$60 \times 0.25 = \$15$, for a sale price of $\$45$, or directly, $\$60 \times 0.75$. A $\$200$ coat marked down $30\%$ and then an additional $15\%$ off drops to $\$200 \times 0.70 = \$140$ and then $\$140 \times 0.85 = \$119$, a total discount of $40.5\%$, not $45\%$, since the combined multiplier is $0.70 \times 0.85 = 0.595$. Three discounts of $10\%$, $20\%$, and $15\%$ combine to a multiplier of $0.9 \times 0.8 \times 0.85 = 0.612$ (an equivalent single discount of $38.8\%$); for present value, $\$1000$ received in $5$ years at a $6\%$ discount rate is worth $PV = 1000/(1.06)^5 = \$747.26$ today.
Key Insight
A discount reduces the price by a percentage of the original, and the sale price can be found in one step by subtracting the discount rate from $100\%$ and multiplying. Sequential discounts multiply rather than add because each successive discount applies to the already-reduced price, and retailers sometimes stack discounts to make sales look larger than they mathematically are, the true combined effect is always the product of the individual multipliers. Present value discounting and price discounting share the same structure, both multiply a base value by a factor less than $1$, and financial discounting reveals the "time value of money," the principle that a dollar today is worth more than a dollar in the future, a foundational concept in corporate finance and investment analysis.