2.3 Commercial Arithmetic

• Simple interest
• Compound interest, yearly and semi-annual
• Appreciation and depreciation
• Hire purchase: deposit, instalments, carrying charge and rate of interest
• Income tax: gross income, taxable income, relief, PAYE and net income

• compute simple interest using the simple interest formula
• derive compound interest formula using the step by step method
• determine compound interest using the compound interest formula
• determine the value of appreciation and depreciation of assets
• determine the cost of goods in hire purchase
• compute income tax using taxation table
• apply commercial arithmetic concepts in day to day life
• appreciate the use of commercial arithmetic in real-life situations

“Why is commercial arithmetic important in our day to day transactions?”

The titles are open to everyone. Reading a lesson needs an account — sign in or create one.

1. Simple interest on a loan
   40 min · 1 practice tasks · quiz
   Use I = P x R x T / 100 on a loan for goods, convert months to years, and find a missing rate or time.
2. From the steps to a formula
   40 min · 1 practice tasks · quiz
   Build the compound-interest formula from one year at a time, and check it against the Grade 8 three-year result.
3. Compound interest for four years
   40 min · 1 practice tasks · quiz
   Use the yearly compound formula for four years, and compare the interest with simple interest on the same principal.
4. Compounding every half-year
   40 min · 1 practice tasks · quiz
   For semi-annual compounding, halve the yearly percent and double the number of periods.
5. Appreciation by the formula
   40 min · 1 practice tasks · quiz
   A value that rises by a fixed percent each year uses the compound formula, so later increases are larger.
6. Depreciation by the formula
   40 min · 1 practice tasks · quiz
   A value that falls by a fixed percent of what remains uses P times (1 - R/100) to the power n, so later falls are smaller.
7. Carrying charge and its rate
   40 min · 1 practice tasks · quiz
   Find the hire-purchase price, name the extra as the carrying charge, and find the simple rate on the unpaid cash balance.
8. Building the instalment
   40 min · 1 practice tasks · quiz
   From a stated simple rate on the unpaid balance, find the carrying charge, the hire-purchase price and each instalment.
9. A classroom tax table
   40 min · 1 practice tasks · quiz
   Work monthly pay through fixed bands, then subtract a personal relief from the tax to get PAYE.
10. PAYE and another deduction
    40 min · 1 practice tasks · quiz
    Build gross income from basic pay and a taxable allowance, then take PAYE and a separate welfare deduction off the net income.
11. The rate on the next slice
    40 min · 1 practice tasks · quiz
    An increase that stays inside the top band is taxed only at the rate of that band, and the relief does not change.
12. Three figures before a choice
    40 min · 1 practice tasks · quiz
    Compare two years of simple interest, two years of compound interest, and a purchase that both depreciates and can be bought on hire purchase.