Time Value of Money

₹100 today is worth more than ₹100 a year from now. This is the most fundamental concept in finance. Money available now can be invested to earn a return, so it is inherently more valuable than the same amount received in the future. Conversely, a future cash flow must be discounted back to its equivalent present value before you can compare it to a present cost.

This principle underlies almost every financial decision: loan pricing, bond valuation, project appraisal, and equity valuation. When a bank offers you a home loan at 9% per annum, it is pricing the time value of your future repayments. When an analyst builds a DCF model, she is applying the same logic at scale.

Understanding compounding, how returns build on previous returns, is equally critical. The Rule of 72 (divide 72 by the interest rate to get approximate doubling time) is a quick mental check on the power of compounding.

Core formulas:

Future Value: FV = PV × (1 + r)^n ₹1,00,000 at 12% for 10 years → FV = ₹1,00,000 × (1.12)^10 = ₹3,10,585

Present Value: PV = FV ÷ (1 + r)^n What is ₹5,00,000 receivable in 5 years worth today at 10%? → PV = ₹5,00,000 ÷ (1.10)^5 = ₹3,10,461

Net Present Value: NPV = Σ [CFt ÷ (1 + r)^t] − Initial Investment If NPV > 0, the project creates value. If NPV < 0, it destroys value at that discount rate.

Annuity (equal periodic payments): PV = PMT × [1 − (1+r)^-n] ÷ r Used for EMI calculations and pension valuation.

Key concepts:

• Discount rate (r): The opportunity cost of capital, what you could earn elsewhere at similar risk.
• Compounding frequency: Monthly compounding at 12% p.a. is not the same as annual compounding. Effective Annual Rate (EAR) = (1 + r/m)^m − 1.
• Real vs Nominal: Nominal rate includes inflation. Real rate ≈ Nominal rate − Inflation rate (Fisher equation).