Percentage Change for Raises and Discounts

A manager says your salary will rise from $52,000 to $56,160. A store advertises 30% off a $90 jacket. Both statements describe a percentage change, but they invite different questions. For the raise, you know the old and new amounts and need the rate. For the jacket, you know the rate and original price and need the new amount. Keeping those two patterns separate prevents most mistakes.

Finding a percentage increase

To find the rate of an increase, subtract the original value from the new value, divide that difference by the original value, then multiply by 100.

Percentage increase = (new value − original value) ÷ original value × 100

For the salary example, the dollar increase is $56,160 − $52,000, or $4,160. Divide $4,160 by the original $52,000 to get 0.08. Multiply by 100, and the raise is 8%. The original number belongs in the denominator because it’s the starting point against which the change is measured.

You can check any old-and-new pair with the Percentage Calculator. This is especially useful when the result isn’t tidy. If rent moves from $1,475 to $1,549, the $74 increase is about 5.02%, not exactly 5%.

Turning a raise rate into dollars

When the percentage is already known, convert it to a decimal and multiply it by the original amount. A 6.5% raise on a $68,000 salary is 0.065 × $68,000, which equals $4,420. Add that increase to the starting salary for a new annual salary of $72,420.

For a rough monthly view, divide the annual increase by 12: $4,420 ÷ 12 is about $368.33 before deductions. That isn’t the same as extra take-home pay. Taxes, retirement contributions, insurance, and other payroll items can change the amount that reaches your bank account. The Loan Payment Calculator can help if you’re deciding how much of the new income could safely go toward a planned car or home payment.

Calculating a sale discount

A discount is a percentage decrease. Multiply the original price by the discount rate to find the dollars saved, then subtract those savings from the original price.

Sale price = original price − (original price × discount rate)

For the $90 jacket at 30% off, the savings are $90 × 0.30 = $27. The sale price is $63. If local sales tax is 7.5%, apply it after the discount: $63 × 0.075 = $4.725, which rounds to $4.73. The checkout total becomes $67.73.

Successive discounts need special care. A 20% discount followed by another 10% discount does not equal 30% off. A $200 item falls to $160 after the first discount, then to $144 after the second. The total savings are $56, or 28% of the original price. Each rate acts on a different base.

Reversing the calculation

Sometimes you see the final amount and need to recover the original. If a $102 item reflects a 15% increase, divide $102 by 1.15. The original was about $88.70. Don’t subtract 15% from $102; that uses the changed value as the base and produces a different answer.

For a discounted item, divide the sale price by the percentage that remains. A $72 chair after 20% off represents 80% of its original price, so $72 ÷ 0.80 gives an original price of $90.

A quick reasonableness check

Estimate before trusting the exact result. Ten percent of $640 is $64, so a 12% increase should be somewhat more than $64; the exact increase of $76.80 makes sense. A 40% discount should leave more than half the price but less than two-thirds. On a $150 purchase, the $90 result fits that range.

Also watch the difference between percentage change and percentage points. If a savings rate rises from 4% of income to 6%, that’s an increase of 2 percentage points, but a 50% relative increase because 2 is half of the original 4. Naming the measure clearly makes salary discussions, price comparisons, and budget decisions much easier to interpret.