Business Mathematics & Finance
Business Mathematics & Finance
This domain tests time value of money, interest, annuities, EMI, NPV and IRR, bond and yield calculations, and business ratios. The exam rewards setting out the formula and converting rates and periods correctly.
Core rules and concepts
- Simple interest = P × r × t. Compound interest uses P(1 + r)^n; more frequent compounding raises the effective annual rate.
- Present value discounts future cash flows: PV = FV ÷ (1 + r)^n. NPV = present value of inflows − initial outflow; accept a project when NPV is positive at the cost of capital.
- IRR is the discount rate making NPV zero; compare it with the hurdle rate. NPV and IRR can rank projects differently when scale or timing differs.
- Ordinary annuity payments occur at period end; annuity due payments occur at period start and are worth more by one period’s interest.
- EMI = P × r × (1 + r)^n ÷ [(1 + r)^n − 1], where r is the monthly rate and n is the number of months.
- Break-even quantity = fixed costs ÷ contribution per unit; contribution = selling price − variable cost per unit.
Worked example
A ₹10 lakh loan carries 12% a year for 24 months. Monthly rate r = 12% ÷ 12 = 1% = 0.01; n = 24. (1.01)^24 ≈ 1.26973. EMI = 1,000,000 × 0.01 × 1.26973 ÷ (1.26973 − 1) ≈ ₹47,074. Total repayment ≈ 47,074 × 24 = ₹1,129,776, so total interest ≈ ₹129,776. Using 12% as the monthly rate would be a serious error.
Traps
Divide the annual rate by the compounding periods per year. Multiply years by periods per year. Do not mix annuity due with ordinary annuity. A higher IRR is not always better if project size differs. Percentage changes use the original base, not the new value.