NBT Quantitative Literacy: Percentages and Financial Mathematics 4

Question 1

A retailer marks up a jacket by 25% above cost price, then offers a 20% discount in a sale. What is the net percentage change in price compared to the original cost price?

Accepted Answer

0% — the price returns exactly to cost

Answer

Applying both changes sequentially: Cost × 1.25 × 0.80 = Cost × 1.00. The two operations cancel exactly, so the final price equals the original cost price — a 0% net change. A common error is to simply subtract 20% from 25% and conclude a 5% increase, but percentage changes must be multiplied, not added or subtracted.

Question 2

R15,000 is invested at 9% per annum compounded monthly. What is the accumulated value after 3 years? (Round to the nearest cent.)

Accepted Answer

R19,629.68

Answer

Using A = P(1 + i/n)^(nt): A = 15,000 × (1 + 0.09/12)^(12×3) = 15,000 × (1.0075)^36. Calculating (1.0075)^36 ≈ 1.308645, so A ≈ R19,629.68. Option A uses simple interest (15,000 + 15,000×0.09×3 = R19,050). Option B compounds annually (15,000×1.09³ ≈ R19,425.44). Monthly compounding yields the highest return because interest is earned on interest more frequently.

Question 3

A customer pays R1,725 for a television set. This price includes VAT at 15%. What is the rand amount of VAT included in the price paid?

Accepted Answer

R225.00

Answer

The VAT-inclusive price equals the ex-VAT price × 1.15. To extract VAT: VAT = R1,725 × (15/115) = R1,725 × (3/23) = R225.00. Option A (R258.75) is the most common error — calculating 15% of the inclusive price (R1,725 × 0.15) instead of reversing the VAT. The VAT fraction must always be 15/115, not 15/100.

Question 4

Thabo earns a nominal interest rate of 11% per annum on his savings account. Annual inflation is 7%. Using the exact Fisher equation, what is his real rate of return?

Accepted Answer

3.74%

Answer

The Fisher equation states: (1 + real rate) = (1 + nominal rate) / (1 + inflation rate). So: (1 + r) = 1.11 / 1.07 ≈ 1.03738, giving r ≈ 3.74%. Option A (4.00%) uses the simple approximation of subtracting inflation from the nominal rate (11% − 7%), which overestimates the real return. Option D incorrectly adds the rates. The exact formula is required for precision.

Question 5

A laptop priced at R9,600 is purchased on hire purchase. A 25% deposit is paid upfront, and the balance is financed over 24 months at 15% per annum simple interest. What is the monthly instalment?

Accepted Answer

R390.00

Answer

Deposit = 25% × R9,600 = R2,400. Balance financed = R9,600 − R2,400 = R7,200. Simple interest on balance = R7,200 × 0.15 × 2 = R2,160. Total to repay = R7,200 + R2,160 = R9,360. Monthly instalment = R9,360 ÷ 24 = R390.00. Option A (R300) forgets to add interest (R7,200 ÷ 24). Option C (R420) incorrectly calculates interest on the full purchase price of R9,600 rather than the financed balance.

(NBT) National Benchmark Test Practice Test

(NBT) National Benchmark Test Practice Test

NBT Quantitative Literacy: Percentages and Financial Mathematics 4