Financial Arithmetic – Money Maths Made Clear
Financial arithmetic applies the four operations to real-life money situations. It is one of the most practically important areas of mathematics.
Merchants have needed reliable ways to calculate profit, interest, and fair prices for as long as trade has existed. One of the earliest surviving arithmetic textbooks aimed squarely at this need is Leonardo of Pisa's (better known as Fibonacci) 1202 book Liber Abaci, which introduced Europe to the Hindu–Arabic numeral system largely through worked examples about currency conversion, profit-sharing between merchants, and interest on loans – practical money problems almost identical in structure to the ones on this page. VAT, a newer addition to the financial-arithmetic toolkit, was first implemented nationally by France in 1954, designed by the French economist Maurice Lauré as a more efficient alternative to the cascading sales taxes it replaced; it has since been adopted by more than 170 countries.
Profit and Loss
Profit = Selling price − Cost price = £110 − £80 = £30.
Profit % = (Profit ÷ Cost price) × 100 = (30 ÷ 80) × 100 = 37.5%.
Simple Interest
I = PRT ÷ 100 = (500 × 4 × 3) ÷ 100
I = 6 000 ÷ 100 = £60.
VAT
Discounts and Sale Prices
Sale price = original × (1 − discount %/100) = 120 × (1 − 0.25)
Sale price = 120 × 0.75 = £90.
Budget Planning
Total income − total expenses = savings. Divide savings by total income and multiply by 100 to find the savings percentage.
Key Takeaways
- Profit = selling price − cost; express as % of cost price.
- Simple interest = PRT/100.
- VAT adds to the price; reverse VAT divides by the multiplier.
- Discounts reduce the price: multiply by (1 − rate).