Time Value of Money Formulas

Understanding the Time Value of Money is crucial in finance. It shows how money's value changes over time, impacting investment decisions. Key formulas like Present Value and Future Value help evaluate opportunities, plan savings, and assess financial growth effectively.

1. Present Value (PV) formula

   • PV = FV / (1 + r)^n
   • Calculates the current worth of a future sum of money based on a specific interest rate.
   • Essential for assessing investment opportunities and financial decisions.
   • Helps in understanding the impact of time on money's value.

2. Future Value (FV) formula

   • FV = PV * (1 + r)^n
   • Determines the value of a current investment at a future date, considering compound interest.
   • Useful for planning savings and investment growth over time.
   • Highlights the importance of interest rates and compounding periods.

3. Present Value of an Annuity (PVA) formula

   • PVA = PMT * [(1 - (1 + r)^-n) / r]
   • Calculates the present value of a series of equal payments made at regular intervals.
   • Important for valuing cash flows from investments like bonds or loans.
   • Assists in retirement planning and understanding loan repayments.

4. Future Value of an Annuity (FVA) formula

   • FVA = PMT * [((1 + r)^n - 1) / r]
   • Determines the future value of a series of equal payments made at regular intervals.
   • Useful for assessing the growth of regular savings or investment contributions.
   • Highlights the effect of compounding on periodic investments.

5. Present Value of a Perpetuity formula

   • PV = PMT / r
   • Calculates the present value of an infinite series of cash flows that occur at regular intervals.
   • Important for valuing investments that provide perpetual cash flows, like certain stocks.
   • Simplifies the analysis of long-term financial instruments.

6. Effective Annual Rate (EAR) formula

   • EAR = (1 + (i/n))^n - 1
   • Represents the actual annual return on an investment, accounting for compounding.
   • Essential for comparing different financial products with varying compounding periods.
   • Helps investors understand the true yield of their investments.

7. Nominal interest rate to effective interest rate conversion

   • Effective Rate = (1 + nominal rate / m)^m - 1
   • Converts nominal interest rates to effective rates based on compounding frequency.
   • Important for accurately assessing the cost of loans and returns on investments.
   • Aids in making informed financial decisions by comparing rates.

8. Compound Annual Growth Rate (CAGR) formula

   • CAGR = (Ending Value / Beginning Value)^(1/n) - 1
   • Measures the mean annual growth rate of an investment over a specified time period.
   • Useful for evaluating the performance of investments and comparing growth rates.
   • Simplifies the understanding of investment returns over time.

9. Net Present Value (NPV) formula

   • NPV = Σ (Cash inflow / (1 + r)^t) - Initial Investment
   • Calculates the difference between the present value of cash inflows and outflows over time.
   • Essential for investment appraisal and project evaluation.
   • A positive NPV indicates a profitable investment opportunity.

10. Internal Rate of Return (IRR) formula

    • IRR is the rate (r) that makes NPV = 0
    • Represents the discount rate at which the present value of cash inflows equals the initial investment.
    • Important for assessing the profitability of potential investments.
    • A higher IRR indicates a more attractive investment opportunity.