45 min readCalculator allowedNeeds: number theory and computation
Try each one on paper first, then check a single step. That is worth far more than reading a finished solution.
Example 1 — percentage profit
An article costs a shopkeeper $800 and is sold for $920. Find the percentage profit.
1Profit =$920−$800=$120Selling price minus cost price.
2Percentage profit =cost priceprofit×100The cost price goes underneath — not the selling price.
3=800120×100
4=15%Dividing by 920 instead would give 13%, which is the classic wrong answer here.
Example 2 — compound interest
$5000 is invested at 6% per annum compound interest for 3 years. Find the amount in the account and the interest earned.
1Amount =P(1+100R)TThis formula gives the total, not the interest.
2=5000×(1.06)31+1006=1.06, and T=3.
3=5000×1.191016=$5955.08That is the amount in the account.
4Interest =$5955.08−$5000=$955.08Subtract the principal. Compare with $900 of simple interest — compounding is worth $55.08 here.
Example 3 — cash price against hire purchase
A television is marked at $3200. A 15% discount is given for cash. Alternatively it may be bought for a deposit of $500 and 12 monthly payments of $260. How much more does the hire purchase cost?
1Cash price =0.85×3200=$2720Paying 85% is quicker than finding 15% and subtracting.
2Instalments =12×$260=$3120Twelve payments, not one.
3Hire purchase total =$500+$3120=$3620The deposit counts — it is money handed over.
4Difference =$3620−$2720=$900That is what the credit costs.