Business Math Formulas Cheat Sheet
The core formulas from a business math course on one page, each with a short example using round numbers. Rates are written as decimals inside formulas (6% = 0.06). Print it or save it as a PDF to keep next to your homework.
Percents
- Portion
- Portion = Base × Rate15% of $240 = $240 × 0.15 = $36.00
- Rate
- Rate = Portion ÷ Base$36 ÷ $240 = 0.15 = 15%
- Base
- Base = Portion ÷ Rate$36 ÷ 0.15 = $240.00
- Percent change
- (New − Old) ÷ Old$50 to $65: $15 ÷ $50 = 0.3 = 30% increase
Trade and series (chain) discounts
- Trade discount
- Trade discount = List price × Rate$480 less 15%: $480 × 0.15 = $72.00
- Net price
- Net price = List price − Trade discount = List price × (1 − Rate)$480 − $72 = $408.00
- Net price equivalent rate
- (1 − d₁) × (1 − d₂) × (1 − d₃) …25/10/5: 0.75 × 0.9 × 0.95 = 0.64125
- Net price, chain
- Net price = List price × Net price equivalent rate$1,200 × 0.64125 = $769.50
- Single equivalent discount rate
- 1 − Net price equivalent rate1 − 0.64125 = 0.35875 = 35.875%
- List price
- List price = Net price ÷ Net price equivalent rate$769.50 ÷ 0.64125 = $1,200.00
Trade discount calculator · Examples with solutions · Worksheet
Cash discounts
- Terms 2/10, n/30
- 2% off if paid within 10 days of the invoice date; the full net price is due within 30 days
- Cash discount
- Cash discount = Net price × Cash discount rate$1,500 invoice, 2/10, n/30, paid on day 8: $1,500 × 0.02 = $30.00
- Amount paid
- Net price − Cash discount = Net price × (1 − Rate)$1,500 − $30 = $1,470.00
- Partial payment
- Amount credited = Partial payment ÷ (1 − Cash discount rate)$588 paid within 10 days: $588 ÷ 0.98 = $600.00 credited
- Balance due
- Net price − Amount credited$1,500 − $600 = $900.00
Take the cash discount on the merchandise amount after any trade discount and returns; leave freight and sales tax out of it.
Cash discount calculator · Examples with solutions · Worksheet
Markup and markdown
- Selling price
- Selling price = Cost + MarkupCost $40, selling price $50: markup $10.00
- Markup on cost
- Markup % on cost = Markup ÷ Cost$10 ÷ $40 = 0.25 = 25%
- Markup on selling price
- Markup % on selling price = Markup ÷ Selling price$10 ÷ $50 = 0.2 = 20%
- Price from markup on cost
- Selling price = Cost × (1 + Markup % on cost)$40 × 1.25 = $50.00
- Price from markup on selling price
- Selling price = Cost ÷ (1 − Markup % on selling price)$40 ÷ 0.8 = $50.00
- Convert cost → selling price
- % on selling price = % on cost ÷ (1 + % on cost)0.25 ÷ 1.25 = 0.2 = 20%
- Convert selling price → cost
- % on cost = % on selling price ÷ (1 − % on selling price)0.2 ÷ 0.8 = 0.25 = 25%
- Markdown
- Markdown = Original selling price − Reduced price; Markdown % = Markdown ÷ Original selling price$80 reduced to $60: $20 ÷ $80 = 0.25 = 25%
Markup and markdown calculator · Examples with solutions · Worksheet · Profit margin vs markup
Simple interest
- Simple interest
- I = P × R × T (T in years)$2,000 at 6% for 9 months: $2,000 × 0.06 × 9/12 = $90.00
- Exact interest
- T = Days ÷ 365$5,000 at 8% for 90 days: $5,000 × 0.08 × 90/365 ≈ $98.63
- Ordinary interest (banker’s rule)
- T = Days ÷ 360$5,000 × 0.08 × 90/360 = $100.00
- Maturity value
- MV = P + I = P × (1 + R × T)$5,000 + $100 = $5,100.00
- Solve for P, R or T
- P = I ÷ (R × T); R = I ÷ (P × T); T = I ÷ (P × R)
Promissory notes and bank discount
- Bank discount
- Bank discount = Maturity value × Discount rate × Time$6,000 simple discount note, 9%, 120 days: $6,000 × 0.09 × 120/360 = $180.00
- Proceeds
- Proceeds = Maturity value − Bank discount$6,000 − $180 = $5,820.00
- Effective rate
- Effective rate = Bank discount ÷ (Proceeds × Time)$180 ÷ ($5,820 × 120/360) ≈ 9.2784%
- Discounting an interest-bearing note
- 1. MV = Face value × (1 + R × T). 2. Discount period = days from the discount date to maturity. 3. Bank discount = MV × Discount rate × Discount period ÷ 360. 4. Proceeds = MV − Bank discount.$4,000 at 7% for 90 days: MV = $4,070.00; discounted at 9% with 60 days left: $4,070 × 0.09 × 60/360 = $61.05; proceeds $4,008.95
Business metrics
- Gross margin
- (Revenue − COGS) ÷ Revenue × 100
- Profit margin
- (Revenue − Total cost) ÷ Revenue × 100
- Customer acquisition cost
- Total acquisition cost ÷ New customers acquired
- Customer lifetime value
- (Average revenue per customer × Gross margin) ÷ Churn rate
- LTV:CAC ratio
- Customer lifetime value ÷ Customer acquisition cost
- Economic order quantity
- EOQ = √(2 × D × S ÷ H)
- Reorder point
- Lead-time demand + Safety stock
- Safety stock
- z × Daily demand standard deviation × √(Lead time in days)
- Inventory carrying cost
- Average inventory value × Carrying-cost rate
- Labor cost percentage
- Total labor cost ÷ Revenue × 100
- Employee turnover cost
- Departures per year × Cost per departure
Notes on this sheet
- Money in the examples is rounded to the nearest cent at the end; percents that do not end are rounded to four decimal places.
- Courses differ on whether to use 365 or 360 days and on when to round. Use your instructor’s rule when it differs.
- Every example on this sheet is recomputed by an automated test before the page is published.