Time Value of Money and Financial Mathematics - Study Guide
This domain tests compounding, discounting, annuities, perpetuities and the time value of money used in loan and investment decisions. Expect numerical questions where the timing of cash flows changes the answer.
Core ideas
- Future value: FV = PV(1+r)^n. Present value: PV = FV/(1+r)^n.
- Ordinary annuity cash flows occur at period end; annuity due cash flows occur at period start. An annuity due is worth more by a factor of (1+r).
- Perpetuity PV = C/r when the cash flow starts one period from now.
- Effective annual rate = (1 + nominal rate/m)^m − 1; it captures compounding within the year.
- Match the rate to the period: monthly rate with monthly periods, annual rate with annual periods.
Worked example
₹10,000 is invested for three years at 8% compounded annually. FV = 10,000 × (1.08)^3 = 10,000 × 1.259712 = ₹12,597.12. Now find the present value of ₹12,000 receivable in two years at 10%: PV = 12,000/(1.10)^2 = 12,000/1.21 = ₹9,917.36. The reasoning: future cash is discounted because money today can be invested; the higher the rate or the longer the wait, the lower the present value.
Traps
Do not use simple interest when compounding is stated. Do not treat an annuity due as an ordinary annuity. Do not divide an annual rate by 12 unless the problem uses monthly compounding. A high IRR is not automatically better if scale and timing differ; for value creation, use NPV.