Time Value of Money

In financial markets, there are many examples of cash flows that occur at some point in the future but which need to be evaluated today. A cash flow in the future has a value today called the present value. Similarly, a cash flow today has a value in the future known as the future value. Present value and future value are determined by the interest rate and the time period elapsed. They are crucial concepts in finance. For example, the price of a bond is the sum of the present value of all the cash flows expected to be generated by the bond in the future, the mark-to-market value of an interest swap is the sum of the present values of all the cash inflows and outflows from the swap in the future, and the value of an option is the present value of the expected payoff of the option at the exercise date.


This course describes the concepts of present value and future value, and the relationship between them. It is essential for understanding the way in which securities and derivatives are priced, and how decisions are made in financial markets.


    On completion of this course, you will be able to:

    Calculate the future value of an investment for a given present value and a given interest rate

    Recognize the relationship between the present value, future value, and discount factor

    Calculate the value of a perpetuity and an annuity

    Use the present value and future value formulas to solve for an unknown rate or number of periods, and distinguish between nominal and real interest rates


    Topic 1: Future Value

    Future Value & Time Value of Money

    Future Value – Example

    Future Value – Simple vs. Compound Interest

    Future Value – A Historical Example

    Topic 2: Present Value

    Calculating Present Value from Future Value

    Present Value – Continuous Compounding

    Present Value – Continuous Compounding – Example

    Present Value of Multiple Cash Flows

    o Example 1

    o Example 2

    Topic 3: Perpetuities & Annuities

    Definition of an Annuity & a Perpetuity

    Valuing Perpetuities

    Valuing Perpetuities - Another Example

    Valuing Annuities

    Valuing Annuities – Example

    Annuities – Calculating Future Value

    Relationship between Perpetuities & Annuities

    Relationship between Perpetuities & Annuities – Example

    Topic 4: Present Value & Future Value – Other Considerations

    Solving for the Interest Rate and the Number of Periods

    Solving for the Rate

    Solving for the Number of Periods



    60 Minutes

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