Financial Mathematics and Consumer Situations
What this domain tests
Financial Mathematics and Consumer Situations applies arithmetic and proportional reasoning to budgeting, costs, interest, taxation, purchasing, and decision-making. The exam presents realistic consumer scenarios and asks you to compute costs and justify a choice.
Core rules and concepts
- Budgeting: balance income against fixed and variable expenses. A balanced budget has income equal to total expenses; a surplus or deficit is the difference.
- Simple interest: $I=Prt$, where $P$ is the principal, $r$ the annual rate as a decimal, and $t$ the time in years. Total amount is $P+I$.
- Compound interest: $A=P(1+\frac{r}{n})^{nt}$, where $n$ is the number of compounding periods per year. More frequent compounding raises the total.
- Taxation: a sales tax is a percentage added to the price; compute it on the discounted price when a discount is applied first, because order matters.
- Purchasing decisions: compare unit prices, account for financing charges, and consider total cost over time rather than sticker price alone.
Worked example
A laptop is listed at $900. A 15% discount applies, then a 9.975% sales tax is added. What is the final price?
Discount: $900\times0.15=135$, so the discounted price is $900-135=765$ dollars.
Tax on the discounted price: $765\times0.09975\approx76.31$ dollars.
Final price: $765+76.31=841.31$ dollars.
Note the trap: applying the discount and tax as a combined rate of $15%+9.975%$ would give a wrong answer. The operations are sequential, and the tax is computed on the reduced price.
Traps that cost marks
- Adding a discount and a tax as if they were a single rate.
- Using a monthly interest rate in a formula that expects an annual rate, or forgetting to convert percent to decimal.
- Computing simple interest when the problem specifies compounding.
- Comparing sticker prices without comparing unit prices or total financing cost.
- Forgetting that a budget deficit is a negative balance, not a zero balance.