Business Mathematics
Business Mathematics tests time value of money, interest, annuities, net present value, break-even analysis, matrices and basic calculus applied to business decisions.
Core rules
- Simple interest = P × r × t; compound amount = P(1 + r)^n.
- Effective annual rate = (1 + r/m)^m − 1 for m compounding periods per year.
- NPV discounts all cash flows at the required return; accept a project with positive NPV.
- Annuity present value factor = [1 − (1 + r)^−n] / r.
- Break-even units = fixed costs / contribution per unit.
Worked example
A project costs 100m now and returns 60m at the end of each of two years. Required return is 10%. PV of year 1 = 60/1.10 = 54.55m. PV of year 2 = 60/1.21 = 49.59m. NPV = −100 + 54.55 + 49.59 = +4.14m. Accept the project because NPV is positive; the IRR is above 10%.
Traps
Do not mix percentage and decimal rates. Do not discount a cash flow at time zero. Use the annuity factor only for equal cash flows. For break-even, use contribution, not selling price. Payback ignores cash flows after payback and the time value of money.