NBT Quantitative Literacy: Percentages and Financial Mathematics Flashcards

A clothing store increases all prices by 30% before a major sporting event, then reduces them by 30% afterwards. A jacket that originally cost R600 is now priced at:

Answer: R546 — the jacket now costs 9% less than the original price

Successive percentage changes do NOT cancel out. R600 × 1.30 = R780 (after increase), then R780 × 0.70 = R546 (after decrease). The net effect is R600 × 1.30 × 0.70 = R600 × 0.91 = R546 — a net decrease of 9%. This is because the 30% decrease is applied to the larger inflated price, so more rands are removed than were originally added.

An investment account offers a nominal annual interest rate of 12%, compounded monthly. The effective annual interest rate is closest to:

Answer: 12.68%

The effective annual rate accounts for monthly compounding: (1 + 0.12/12)^12 − 1 = (1.01)^12 − 1 ≈ 1.12683 − 1 = 12.68%. The 12.00% is the stated nominal rate. The 12.36% is what you get with semi-annual compounding: (1.06)^2 − 1. More frequent compounding always yields a higher effective rate than the nominal rate.

A price tag shows R460.00 including 15% VAT. A student calculates the VAT component as R460 × 15% = R69.00. Which statement is correct?

Answer: The student is incorrect; the VAT amount is R60.00, calculated as R460 ÷ 1.15 × 15%

R460 already includes VAT, meaning it represents 115% of the original price. The pre-VAT price is R460 ÷ 1.15 = R400. The VAT is therefore R460 − R400 = R60, or equivalently R400 × 15% = R60. The student's error was applying 15% to the VAT-inclusive price, which overstates the VAT. Note that R460 × (15/115) = R60 exactly, which is an equivalent shortcut.

A machine is purchased for R180,000. Company A uses the straight-line depreciation method at 20% of original cost per year. Company B uses the reducing-balance method at 20% per year. After 4 years, which statement about the book values is correct?

Answer: Company B's machine has a higher book value by R37,728

Straight-line (Company A): 20% × R180,000 = R36,000 depreciation per year. After 4 years: R180,000 − (4 × R36,000) = R36,000. Reducing-balance (Company B): R180,000 × (0.80)^4 = R180,000 × 0.4096 = R73,728. Company B's machine retains a higher book value: R73,728 − R36,000 = R37,728 more. The reducing-balance method slows depreciation over time, so the asset retains more value in later years compared to straight-line.

A South African student is awarded a USD scholarship of $5,000 when the exchange rate is R17.00 per dollar. By the time the funds are transferred, the rand has strengthened by 4% against the dollar. How many rands does the student actually receive?

Answer: R81,730.77 — the stronger rand means fewer rands per dollar

A stronger rand means each dollar buys fewer rands. If the rand strengthens by 4%, the new exchange rate is R17.00 ÷ 1.04 ≈ R16.346 per dollar. The student receives $5,000 × R16.346 ≈ R81,730.77. A common error is to calculate R85,000 × 0.96 = R81,600 (subtracting 4% instead of dividing by 1.04). This distinction matters: a 4% strengthening means the new rate is the old rate divided by 1.04, not multiplied by 0.96.

A television has a cash price of R6,000. The hire purchase agreement requires a 10% deposit, with the balance settled in 12 equal monthly instalments. If the total hire purchase price is 20% more than the cash price, what is the monthly instalment?

Answer: R550 — found by subtracting the deposit from the total HP price, then dividing by 12

Total HP price = R6,000 × 1.20 = R7,200. Deposit = 10% × R6,000 = R600. The remaining balance to be paid in instalments = R7,200 − R600 = R6,600. Monthly instalment = R6,600 ÷ 12 = R550. The most common error is dividing the full HP price by 12 (giving R600) without first deducting the upfront deposit, which has already been paid.