Time Value of Money — PSX Investing

PSX Investing

By PSX Investing • Sep 07, 2025

Time Value of Money (TVM): Concepts, Formulas & Examples

A clear, practical guide to understanding present value, future value, annuities, and how to apply TVM in investing and personal finance.

1. What is the Time Value of Money?

The Time Value of Money (TVM) states that a sum of money today is worth more than the same sum in the future. The reason is simple: today’s money can be invested to earn returns (interest, dividends, capital gains). Inflation also diminishes future purchasing power.

2. Why TVM Matters

TVM underpins almost every financial decision: valuing bonds, pricing investments, comparing cash-flow streams, deciding whether to take a lump sum or annuity, and evaluating projects (NPV, IRR).

3. Core Formulas

3.1 Future Value (FV)

Formula: FV = PV × (1 + r)ⁿ
Where PV = present value, r = interest rate per period, n = number of periods.

3.2 Present Value (PV)

Formula: PV = FV / (1 + r)ⁿ
Use this to discount future cash flows to present terms.

3.3 Annuities (PV & FV)

PV of an ordinary annuity:

PV = P × (1 - (1 + r)^-n) / r

FV of an ordinary annuity:

FV = P × ((1 + r)ⁿ - 1) / r

(P = payment per period)

3.4 Perpetuity

Perpetuity (constant payment forever):

PV = P / r

Example: A perpetual dividend of $100 at 5% → PV = 100 / 0.05 = $2,000.

4. Worked Examples

Example 1 — Future Value

Invest $1,000 at 8% annually for 5 years.

Calculation: FV = 1,000 × (1 + 0.08)⁵ = 1,469.33

Example 2 — Present Value

You are promised $5,000 in 3 years. Discount rate = 10%.

Calculation: PV = 5,000 / (1 + 0.10)³ = 3,756.57

Example 3 — Present Value of an Annuity

Receive $2,000 per year for 5 years, discount rate 6%.

Calculation: PV = 2,000 × (1 - (1 + 0.06)^-5) / 0.06 = 8,416.20

Example 4 — Perpetuity

A stock pays $50 per year forever. Required return = 5%.

PV: 50 / 0.05 = 1,000

5. Practical Applications

Loan amortization: TVM is used to compute monthly payments and outstanding balances.
Bond valuation: Discount coupon payments and principal to find fair price.
Capital budgeting (NPV & IRR): Discount project cash flows to assess viability.
Retirement planning: Calculate how much to save now to meet future income goals.

6. Caveats & Tips

1. Use consistent compounding: If interest is compounded monthly, convert annual rates to monthly (r/12) and use periods n×12.

2. Estimation risk: Future rates are uncertain — be conservative with assumptions or run sensitivity checks.

3. Real vs nominal rates: Adjust for expected inflation when needed. Real rate ≈ (1 + nominal)/(1 + inflation) – 1.

7. Conclusion

Time Value of Money is a foundational concept in finance — essential for comparing cash flows across time, valuing investments, and making informed financial decisions. Mastering PV and FV calculations unlocks better choices for investing, borrowing and planning.