Chapter 5

Chapter 5: Time Value of Money Concepts

Key Concepts

  • Time Value of Money: Money can earn interest, meaning it's worth more now than in the future.

  • Future Value (FV): The value of an investment at a specific date in the future based on an assumed rate of growth over time.

  • Present Value (PV): The current worth of an amount regarding future cash flows, discounted at the appropriate interest rate.

Types of Interest

  • Simple Interest: Interest calculated only on the principal amount of a loan or investment.

    • Formula: Simple Interest = Principal × Rate × Time

  • Compound Interest: Interest calculated on the initial principal, which also includes all the accumulated interest from previous periods.

    • Example: If $1,000 is invested at 10% for 3 years, the future value can be calculated using accumulated interest.

Calculating Future and Present Values

  • FV of a Single Amount: FV = I(1 + i)^n

    • I = investment amount, i = interest rate, n = number of periods.

  • PV Calculation: PV = FV / (1 + i) ^ n

    • This calculation finds the current equivalent of future cash.

Effective Interest Rate

  • Effective Rate: Actual rate at which money grows yearly based on compounding. For example, an annual rate of 12% compounded monthly will have a different effective annual rate.

Annuities

  • Ordinary Annuity: Payments are made at the end of each period.

  • Annuity Due: Payments are made at the beginning of each period.

  • Future Value of Annuity: The total value of a series of equal payments at the end of a specific period, influenced by interest.

  • Present Value of Annuity: Present worth of a series of future payments.

Applications Example

  • Investment Planning: Evaluating whether to choose $740 now or $1,000 three years from now based on time value computations and interest rates.

  • Loans and Payments: Understanding how to structure loan repayments, determine installment amounts, and valuate cash flows.

Excel Functions

  • FV Function: =FV(rate, nper, pmt, [pv], [type])

  • PV Function: =PV(rate, nper, pmt, [fv], [type])

  • Functions can calculate future and present values automatically.