Business Math
"Future Entrepreneur! Pera-pera lang yan. Master interest, discounts, and pricing strategies para kumita ang negosyo!"
1. Simple Interest - The Basic Formula 💰
I = P × r × t
F = P + I = P(1 + rt)
Simple interest is calculated only on the original principal amount throughout the entire loan or investment period.
| Variable | Meaning | Example |
|---|---|---|
| I | Interest earned/paid | ₱1,500 |
| P | Principal (original amount) | ₱10,000 |
| r | Rate (as decimal) | 5% = 0.05 |
| t | Time (in years) | 3 years |
| F | Future Value / Maturity Value | ₱11,500 |
📌 Example Problem:
Maria deposits ₱50,000 in a bank at 6% simple interest for 2 years. How much interest will she earn?
Solution: I = P × r × t = ₱50,000 × 0.06 × 2 = ₱6,000
Maturity Value: F = ₱50,000 + ₱6,000 = ₱56,000
Time Conversion (Important!):
- • If time is in months: t = months ÷ 12
- • If time is in days (Ordinary): t = days ÷ 360
- • If time is in days (Exact): t = days ÷ 365
2. Compound Interest - Money That Grows Money 📈
F = P(1 + r/n)nt
Where n = compounding frequency per year
Compound interest is calculated on both the principal AND the accumulated interest from previous periods. This is why it grows faster!
| Compounding | n value | Formula becomes |
|---|---|---|
| Annually | n = 1 | F = P(1 + r)t |
| Semi-annually | n = 2 | F = P(1 + r/2)2t |
| Quarterly | n = 4 | F = P(1 + r/4)4t |
| Monthly | n = 12 | F = P(1 + r/12)12t |
| Daily | n = 365 | F = P(1 + r/365)365t |
📌 Example: Simple vs Compound Comparison
₱100,000 at 10% for 3 years:
Simple Interest:
F = 100,000(1 + 0.10 × 3) = ₱130,000
Interest = ₱30,000
Compound (Annually):
F = 100,000(1.10)3 = ₱133,100
Interest = ₱33,100
Compound earns ₱3,100 more - that's the power of compounding!
3. Mark-up and Selling Price 🏷️
Mark-up is the amount added to the cost to determine the selling price.
Based on COST:
Selling Price = Cost + Mark-up
SP = C + (C × Mark-up Rate)
SP = C(1 + MR)
Mark-up Rate (on Cost):
MR = (SP - C) ÷ C
MR = Mark-up ÷ Cost
📌 Example:
A shirt costs ₱200. The store applies a 50% mark-up. What is the selling price?
Solution:
Mark-up = ₱200 × 0.50 = ₱100
SP = ₱200 + ₱100 = ₱300
Or: SP = ₱200(1 + 0.50) = ₱200(1.50) = ₱300
4. Gross Profit Margin (Margin Based on Selling Price) 💹
Margin is mark-up expressed as a percentage of selling price (not cost). This is important for financial reporting!
Gross Profit Margin:
Margin = (SP - Cost) ÷ SP × 100%
Mark-up (on Cost)
Mark-up Rate = Profit ÷ Cost
Example: Cost ₱100, SP ₱150
Mark-up = 50 ÷ 100 = 50%
Margin (on SP)
Margin = Profit ÷ SP
Example: Cost ₱100, SP ₱150
Margin = 50 ÷ 150 = 33.33%
💡 Conversion Formulas:
- • Margin to Mark-up: Mark-up = Margin ÷ (1 - Margin)
- • Mark-up to Margin: Margin = Mark-up ÷ (1 + Mark-up)
5. Trade Discounts and Chain Discounts 🏪
Discounts reduce the list price. Chain discounts are multiple discounts applied sequentially.
Single Discount:
Net Price = List Price × (1 - Discount Rate)
Chain Discounts (e.g., 20/10/5):
Net Price = List Price × (1 - d₁) × (1 - d₂) × (1 - d₃)
📌 Example: Chain Discount
List Price: ₱10,000 with discounts of 20%, 10%, 5%
Solution:
Net = ₱10,000 × 0.80 × 0.90 × 0.95
Net = ₱10,000 × 0.684 = ₱6,840
Note: 20/10/5 ≠ 35%! Single equivalent = 31.6%
Single Equivalent Rate (SER):
SER = 1 - [(1-d₁)(1-d₂)(1-d₃)]
For 20/10/5: SER = 1 - 0.684 = 0.316 or 31.6%
6. Annuities - Regular Payments 📅
An annuity is a series of equal payments made at regular intervals.
Ordinary Annuity
Payments at END of each period
Examples: Loan payments, rent
Annuity Due
Payments at BEGINNING of each period
Examples: Insurance premiums, tuition
Future Value of Ordinary Annuity:
FV = PMT × [(1 + r)n - 1] ÷ r
Present Value of Ordinary Annuity:
PV = PMT × [1 - (1 + r)-n] ÷ r
💡 Key Terms:
- • PMT = Regular payment amount
- • r = Interest rate per period
- • n = Total number of payments
7. Business Ratios and Break-Even Analysis 📊
Essential calculations for business decision-making.
Break-Even Point:
BEP (units) = Fixed Costs ÷ (Selling Price - Variable Cost per unit)
BEP (₱) = Fixed Costs ÷ Contribution Margin Ratio
| Ratio | Formula | Use |
|---|---|---|
| Current Ratio | Current Assets ÷ Current Liabilities | Liquidity (should be > 1) |
| Gross Profit Rate | (Sales - COGS) ÷ Sales | Profitability |
| Net Profit Rate | Net Income ÷ Sales | Overall profitability |
| Contribution Margin | (SP - Variable Cost) ÷ SP | Covers fixed costs |
📌 Break-Even Example:
Fixed Costs: ₱100,000 | SP: ₱50 | Variable Cost: ₱30
BEP = 100,000 ÷ (50 - 30) = 100,000 ÷ 20 = 5,000 units
📝 Practice Questions
1. Calculate the simple interest on ₱25,000 at 8% for 18 months.
Show Answer
I = 25,000 × 0.08 × 1.5 = ₱3,000
2. A product costs ₱400 and sells for ₱600. What is the mark-up rate and gross margin?
Show Answer
Mark-up = 200 ÷ 400 = 50%. Margin = 200 ÷ 600 = 33.33%
3. ₱5,000 compounded annually at 6% for 4 years. What is the future value?
Show Answer
F = 5,000(1.06)4 = 5,000 × 1.2625 = ₱6,312.38
4. List price ₱8,000 with chain discounts 15/10. What is the net price?
Show Answer
Net = 8,000 × 0.85 × 0.90 = ₱6,120
💡 ABM Exam Tips
- ✓ Convert percentages to decimals before calculating
- ✓ Watch the time units - convert months/days to years for interest
- ✓ Mark-up vs Margin - know the difference! Different denominators
- ✓ Chain discounts - multiply complements, not add percentages
- ✓ Compound interest - identify n (compounding frequency) carefully
- ✓ Break-even - contribution margin = SP minus variable cost
Test Your Knowledge! 🧠
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