📘 2.1 Time Value of Money
The Time Value of Money (TVM) means that a sum of money is worth more today than the same amount in the future, because money has the potential to earn returns.
Would you prefer to receive ₹100 today or ₹100 after a month? Most people prefer money now, because it can be invested to grow, spent to fulfill immediate needs, or used to reduce debt costs.
This preference — for present money over future money — arises from:
- 🎯 Human tendency for immediate consumption
- 📈 Opportunity to earn interest or returns
- ⚠️ Uncertainty about future payments
Receiving ₹100 today and investing it at 6% annual return will give you ₹100.50 after a month (approx). So, if someone offers you ₹100 after a month instead of now, they must compensate you — at least ₹0.50 — for waiting. This is the essence of TVM.
- Future values must be discounted to compare with today
- Present values can be compounded to estimate future value
- The farther in the future a cash flow is, the lower its value today
- A higher interest rate lowers the present value of future amounts
- The meaning and importance of Time Value of Money
- The difference between present value and future value
- How discounting and compounding work
- Practical examples of TVM in daily finance and investment
📘 2.2 Time Value of Money – Detailed Calculations (Excel Based)
🧾 2.2.1 Present Value (PV)
What it tells you: How much is a future amount worth today?
Why it’s important: It helps compare future payouts with today’s costs, like deciding whether to take ₹1,00,000 today or ₹1,20,000 in 3 years.
Real Scenario: You’re promised ₹6,500 every year for 8 years. If investments earn 7% return, how much is that stream worth today?
Excel Formula: =PV(0.07, 8, -6500)
- 0.07: Interest rate (7%)
- 8: Number of years
- -6500: Cash inflow (negative because it’s money received)
Answer: ₹38,813.44
Conclusion: If you invest ₹38,813.44 today at 7%, you’ll get ₹6,500/year for 8 years.
📈 2.2.2 Future Value (FV)
What it tells you: How much will your investments grow into?
Why it’s important: Helps estimate future value of SIPs or recurring savings.
Real Scenario: You invest ₹5,000 per year for 5 years at 8%. How much will it become?
Excel Formula: =FV(0.08, 5, -5000)
- 0.08: Annual return
- 5: Years
- -5000: Investment per year
Answer: ₹29,336.48
Conclusion: SIPs grow over time — starting early multiplies this effect.
📊 2.2.3 Rate of Return (CAGR)
What it tells you: Annualized return rate between two amounts over time.
Why it’s important: Helps compare mutual funds, stocks, and investment options.
Real Scenario: ₹100 invested grows to ₹120 in 2 years. What’s the annual growth rate?
Excel Formula: =RATE(2,, -100, 120)
- 2: Years
- -100: Initial investment
- 120: Final value
Answer: 9.54%
Conclusion: CAGR provides a true annualized growth rate — key for comparing investments.
💸 2.2.4 Periodic Payment (PMT)
What it tells you: Your EMI or regular SIP needed to meet a goal or repay a loan.
Real Scenario: You take a ₹30 lakh home loan @6.5% for 20 years. What will your EMI be?
Excel Formula: =PMT(0.065/12, 240, -3000000)
- 0.065/12: Monthly interest rate
- 240: Tenure in months (20×12)
- -3000000: Loan principal
Answer: ₹22,367/month
Conclusion: PMT helps plan your EMIs without over-stretching cash flow.
📆 2.2.5 NPER (Loan Tenure)
What it tells you: How many periods (months/years) it’ll take to repay a loan or reach a goal.
Real Scenario: You pay ₹12,000/month to clear a ₹5L loan @8%. How long will it take?
Excel Formula: =NPER(0.08/12, -12000, 500000)
- 0.08/12: Monthly interest rate
- -12000: Monthly payment
- 500000: Loan principal
Answer: 49 months (approx. 4 years 1 month)
Conclusion: NPER helps assess how fast you can reach a goal or repay debt.
📥 2.2.6 Ordinary Annuity
What it is: Recurring payments made at the end of each period (e.g. salary invested monthly).
Example: ₹5,000/year invested for 4 years @10%.
Excel Formula: =PV(0.1, 4, -5000, , 0)
Answer: ₹15,849.33
Conclusion: Annuities are used in pensions, insurance, systematic investing.
📤 2.2.6 Annuity Due
What it is: Recurring payments made at the beginning of each period (e.g. school fee in advance).
Same inputs, but with type = 1 (beginning).
Excel Formula: =PV(0.1, 4, -5000, , 1)
Answer: ₹17,434.26
Conclusion: Annuity Due has more compounding, so higher value than ordinary annuity.
♾️ 2.2.7 Perpetuity
What it is: Fixed income stream that lasts forever. Used for trusts, charitable funds, pensions.
Formula: PV = C / r
Example: If ₹10,000 is received every year and return rate is 8%, then:
Excel/Manual: =10000 / 0.08
Answer: ₹1,25,000
Conclusion: Great for valuing infinite returns like preference shares or foundations.
