Algebra & Numerical Reasoning
Financial Math
Calculating simple and compound interest, profit/loss, and markups/markdowns.
Questions appear in government budget analysis, loan evaluation, and public sector procurement contexts.
What the exam tests
Multi-Period Loan Repayment
Calculate total sum repaid at the end of a loan term using compound interest (interest on interest).
Fluctuating Growth Calculations
Year-over-year percentage changes: multiply the principal by each successive percentage factor sequentially.
Competitive Pricing Comparisons
Compare markup vs. markdown pricing strategies to determine which produces the lower final price.
System Cost Analysis
Layered discounts (e.g., 15% then 10%) plus fixed fees: calculate the final cost after all reductions and additions.
Venture Profitability Analysis
Compare investments by calculating Profit Margin (Profit ÷ Revenue) and ROI (Gain − Cost) ÷ Cost × 100.
Reverse Solving for Investment Variables
Given earned interest and time, use algebraic isolation to find the unknown principal or rate of return.
Fixed and Variable Cost Structure
Calculate total monthly business cost by combining fixed expenses (rent) with variable production costs.
Formula Application
Key rules
- ›Compound interest: P × (1 + i)^n. For fluctuating rates, multiply each year's factor in sequence. Never average the rates.
- ›Profit: Revenue − Expenditure.
- ›ROI: (Gain − Cost) ÷ Cost × 100.
- ›Gross Profit = before taxes; Net Profit = after all costs and taxes. Know which one the question asks for.
Common traps
- !Averaging fluctuating interest rates instead of multiplying successive factors gives the wrong compound total.
Multi-Step Percentages and Unit Standardization
Key rules
- ›Layered discounts: apply the first discount to get a new base, then apply the second discount to that result. Never add the two percentages together.
- ›Convert interest periods to yearly format before applying formulas (e.g., 4 months = 1/3 of a year).
- ›Nominal value is the face value; real value adjusts for inflation. Confirm which the question requires.
Common traps
- !A 15% discount followed by a 10% discount is NOT a 25% discount. It results in a 23.5% total reduction.
Algebraic Isolation, Data Filtering, and Estimation
Key rules
- ›To find an unknown principal or rate, rearrange the formula algebraically and isolate the variable.
- ›Ignore irrelevant figures (names, dates, non-contributing costs) before building the equation.
- ›Use mental rounding to confirm the answer is financially reasonable before finalizing.
Try one
A county borrows $10,000 at 10% annual compound interest for 3 years. What total amount must it repay at the end of the loan?
$10,000 × 1.10³ = $10,000 × 1.331 = $13,310. Compound interest applies interest on accumulated interest each year, not just on the original principal.
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