What is Business Mathematics in A/L Examination (Sri Lanka)?

Business Mathematics is a topic in the Commerce Stream syllabus of A/L Examination (Sri Lanka). It carries a weight of 3% in the exam. Our notes cover the key concepts, formulas, and problem-solving approaches you need to master this topic.

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Business Mathematics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Business Mathematics — Key Facts for Sri Lanka A/L Examination

Simple Interest vs. Compound Interest:

Type	Formula	Use
Simple Interest	I = P × R × T / 100	Short-term loans, bonds
Compound Interest	A = P(1 + R/100)^T	Savings, long-term investments

Annuities:

Future Value of Regular Payments: FV = PMT × [(1+r)^n - 1] / r
Present Value of Regular Payments: PV = PMT × [1 - (1+r)^-n] / r

** hire Purchase**:

Installment = (Cash Price × R/100 × T/12 + Cash Price) / (T × No. of installments)
Interest = Total Amount Paid - Cash Price

⚡ A/L Exam Tip: Always identify if the question asks for simple or compound interest — using the wrong formula loses marks quickly!

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Business Mathematics — Detailed Study Guide

Simple Interest

Formula:

Simple Interest (I) = P × R × T / 100

Where:
P = Principal (Rs.)
R = Rate per annum (%)
T = Time in years

Amount (A) = P + I
A = P + (P × R × T / 100)
A = P[1 + (R × T / 100)]

Example (Sri Lankan context):

Question: Kasun deposits Rs. 50,000 in a fixed deposit at Bank of Ceylon at 12% p.a. simple interest for 3 years. Find the interest earned and the amount.

Solution:
P = Rs. 50,000, R = 12%, T = 3 years
I = 50,000 × 12 × 3 / 100 = Rs. 18,000
A = 50,000 + 18,000 = Rs. 68,000

Variations in Time Period:

Period	T Value
Months	T/12
Days	T/365 (for Sri Lankan banking)
Years and months	T + M/12

Compound Interest

Formula:

Amount (A) = P × (1 + R/100)^T
Compound Interest (CI) = A - P

Where n = number of compounding periods per year:
A = P × (1 + R/n×100)^n×T

Example:

Question: Rs. 100,000 invested at 10% p.a. compound interest for 3 years. Find amount.

Year 1: 100,000 × 1.10 = 110,000
Year 2: 110,000 × 1.10 = 121,000
Year 3: 121,000 × 1.10 = 133,100

Or: A = 100,000 × (1 + 10/100)^3 = Rs. 133,100
CI = 133,100 - 100,000 = Rs. 33,100

Compound Interest vs. Simple Interest Comparison:

Year	SI Amount	CI Amount
1	110,000	110,000
2	120,000	121,000
3	130,000	133,100
5	150,000	161,051

⚡ Key Insight: Over time, compound interest grows faster because interest is earned on previously accumulated interest.

Half-Yearly/Quarterly Compounding:

Annual rate 12%, compounded half-yearly:
Rate per half-year = 6%
Number of periods = 3 × 2 = 6
A = P × (1 + 6/100)^6

Annuities

Ordinary Annuity (payment at end of period):

Future Value (FV) = PMT × [(1+r)^n - 1] / r

Present Value (PV) = PMT × [1 - (1+r)^-n] / r

Where:
PMT = Regular payment
r = Interest rate per period
n = Number of periods

Example:

Question: Regular payment of Rs. 10,000 at end of each year for 5 years at 10% p.a.
Find the Future Value and Present Value.

r = 10% = 0.10, n = 5

FV = 10,000 × [(1.10)^5 - 1] / 0.10
   = 10,000 × [1.61051 - 1] / 0.10
   = 10,000 × 0.61051 / 0.10
   = 10,000 × 6.1051 = Rs. 61,051

PV = 10,000 × [1 - (1.10)^-5] / 0.10
   = 10,000 × [1 - 0.62092] / 0.10
   = 10,000 × 0.37908 / 0.10
   = 10,000 × 3.7908 = Rs. 37,908

Annuity Due (payment at beginning of period):

FV = PMT × [(1+r)^n - 1] / r × (1+r)
PV = PMT × [1 - (1+r)^-n] / r × (1+r)

Hire Purchase and Installment Buying

Key Terms:

Term	Meaning
Cash Price	Price if paying immediately
Deposit/Down Payment	Initial amount paid upfront
Installment	Regular payment amount
Number of installments	How many payments
Interest	Cost of credit

Interest Calculation (Flat Rate Method):

Total Interest = (Cash Price - Deposit) × R/100 × T
Amount to be financed = Cash Price - Deposit
Each Installment = (Amount financed + Interest) / Number of installments

Example:

Question: A fridge has cash price Rs. 80,000. Hire purchase terms: 20% deposit,
balance in 12 monthly installments at 15% p.a. flat rate.
Find the installment amount.

Deposit = 80,000 × 20% = Rs. 16,000
Amount financed = 80,000 - 16,000 = Rs. 64,000
Interest = 64,000 × 15% × 1 = Rs. 9,600
Total to be paid = 64,000 + 9,600 = Rs. 73,600
Monthly installment = 73,600 / 12 = Rs. 6,133.33

Effective Interest Rate (A/L important concept):

Effective Rate = (2 × Flat Rate × Number of years) / (Number of years + 1)

For flat rate 15% over 1 year:
Effective Rate = (2 × 15 × 1) / 2 = 15%
For flat rate 15% over 2 years:
Effective Rate = (2 × 15 × 2) / 3 = 10 × 2 / 3 = 20%
Note: Effective rate is HIGHER than flat rate for multi-year periods

⚡ A/L Exam Tip: Questions on effective interest rate and finding the true cost of hire purchase are popular A/L questions. Sri Lankan consumers often misunderstand hire purchase costs!

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Business Mathematics — Complete Notes for A/L Sri Lanka

Depreciation

Straight Line Method:

Depreciation per year = (Cost - Salvage Value) / Useful Life
Depreciation per year = (Cost - Scrap Value) / Number of years

Book Value at end of Year n = Cost - (Depreciation × n)

Example:

Machine purchased for Rs. 500,000. Salvage value Rs. 50,000. Useful life 5 years.
Depreciation per year = (500,000 - 50,000) / 5 = Rs. 90,000

Year | Book Value (Start) | Depreciation | Book Value (End)
-----|---------------------|--------------|-------------------
1    | 500,000            | 90,000      | 410,000
2    | 410,000            | 90,000      | 320,000
3    | 320,000            | 90,000      | 230,000
4    | 230,000            | 90,000      | 140,000
5    | 140,000            | 90,000      | 50,000

Reducing Balance Method (Declining Balance):

Depreciation rate = 1 - (Salvage/Cost)^(1/n)
Depreciation = Book Value × Rate

Example:

Cost = Rs. 500,000, Salvage = Rs. 50,000, n = 5 years
Rate = 1 - (50,000/500,000)^(1/5) = 1 - (0.10)^0.2 = 1 - 0.6309 = 0.3691 = 36.91%

Year | Book Value (Start) | Depreciation | Book Value (End)
-----|---------------------|--------------|-------------------
1    | 500,000            | 184,550     | 315,450
2    | 315,450            | 116,357     | 199,093
3    | 199,093            | 73,461      | 125,632
4    | 125,632            | 46,346      | 79,286
5    | 79,286             | 29,236      | 50,050 (≈50,000)

Sum of Years’ Digits Method:

SYD = n(n+1)/2 = 5(6)/2 = 15
Depreciation Year 1 = (Cost - Salvage) × 5/15
Depreciation Year 2 = (Cost - Salvage) × 4/15
And so on...

Unit of Output Method:

Depreciation per unit = (Cost - Salvage) / Total units expected
Total depreciation = Depreciation per unit × Units produced in year

Data Interpretation and Business Statistics

Index Numbers (Important for Sri Lankan context):

Simple Price Index:

Price Index = (Price in current year / Price in base year) × 100

Laspeyres Index (Using base year quantities):

L = Σ(Pn × Q0) / Σ(P0 × Q0) × 100

Where:
Pn = Current year price
P0 = Base year price
Q0 = Base year quantity

Paasche Index (Using current year quantities):

P = Σ(Pn × Qn) / Σ(P0 × Qn) × 100

Where:
Qn = Current year quantity

Example:

Item      | Base Year (P0, Q0) | Current Year (Pn, Qn)
----------|--------------------|--------------------
Rice      | Rs. 80/kg, 10 kg   | Rs. 100/kg, 12 kg
Dhal      | Rs. 150/kg, 5 kg   | Rs. 200/kg, 6 kg
Mince     | Rs. 600/kg, 3 kg   | Rs. 700/kg, 4 kg

Laspeyres = (100×10 + 200×5 + 700×3) / (80×10 + 150×5 + 600×3) × 100
         = (1000 + 1000 + 2100) / (800 + 750 + 1800) × 100
         = 4100 / 3350 × 100 = 122.39

Paasche = (100×12 + 200×6 + 700×4) / (80×12 + 150×6 + 600×4) × 100
        = (1200 + 1200 + 2800) / (960 + 900 + 2400) × 100
        = 5200 / 4260 × 100 = 122.07

Consumer Price Index (CPI) - Sri Lanka:

Measures inflation
Based on household consumption patterns
Published by Department of Census and Statistics
Base year periodically updated
Components: Food, Housing, Transport, Health, Education, etc.

Interpreting CPI in Sri Lanka:

CPI Change	Interpretation
CPI increases	Inflation (prices rising)
CPI decreases	Deflation (rare in Sri Lanka)
High CPI	Cost of living increases

Ratios and Proportions in Business

Ratio Analysis in Commerce:

Ratio	Formula	Sri Lankan Context
Current Ratio	CA / CL	Sri Lankan banks prefer 1.5:1+
Quick Ratio	(CA-Stock) / CL	Minimum 1:1 for creditworthiness
Debt Ratio	Debt / Total Assets	Lower = less risky
Interest Coverage	EBIT / Interest	Higher = can service debt

Commission and Brokerage:

Commission = Sale Value × Rate
Net Amount = Sale Value - Commission

Example:
Selling price = Rs. 500,000
Commission rate = 3%
Commission = 500,000 × 3% = Rs. 15,000
Net amount = Rs. 485,000

Profit Sharing Ratios:

Ratio expressed as a:b:c
Total parts = a + b + c
Share = (Ratio part / Total parts) × Total profit

Simultaneous Equations in Business

Business Applications:

Break-even using linear equations:

Revenue line: y = Selling price per unit × x
Cost line: y = Fixed cost + Variable cost per unit × x
Break-even: Solve for x where lines intersect

Pricing decisions:

Supply equation: Qs = a + bP (Supply curve)
Demand equation: Qd = c - dP (Demand curve)
Equilibrium: Qs = Qd → solve for P and Q

Example - Equilibrium Price:

Demand: Qd = 100 - 2P
Supply: Qs = 20 + 3P
At equilibrium: 100 - 2P = 20 + 3P
100 - 20 = 3P + 2P
80 = 5P
P = Rs. 16 (Equilibrium price)
Q = 100 - 2(16) = 68 units

Percentages in Business

Markup vs. Markdown:

Concept	Formula
Cost Price	The price at which seller buys
Selling Price	The price at which seller sells
Markup on Cost	(Profit / CP) × 100
Markup on SP	(Profit / SP) × 100
Markdown	(Reduction from SP) / Original SP × 100

Example:

A shirt costs Rs. 800. It is sold for Rs. 1,000.
Markup on Cost = (200 / 800) × 100 = 25%
Markup on Selling Price = (200 / 1,000) × 100 = 20%

⚡ A/L Exam Tip: Questions on profit percentage frequently confuse students. Always check whether the base is Cost Price or Selling Price. In Sri Lanka, markup is typically calculated on cost price unless specified otherwise.

Discount Calculations:

Trade Discount: Usually a percentage off the catalogue/list price
  - Applied before cash discount
  - Not recorded separately in books

Cash Discount: For early payment
  - Recorded as discount allowed/received
  - e.g., 2/10 net 30

Example:
Invoice: Rs. 100,000
Trade discount: 20%
Cash discount: 5/10 net 30

Step 1: 100,000 - 20% = 80,000 (after trade discount)
Step 2: If paid within 10 days = 80,000 - 5% = Rs. 76,000
Step 3: If not paid within 10 days = Rs. 80,000 (within 30 days)

⚡ A/L Key: Remember the sequence — trade discount applied first, THEN cash discount. Failing this sequence is a common mistake that loses easy marks!

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