Skip to content

CFA Level I · CFA Level I Exam

The Time Value of Money in Finance for CFA Level I

Time value of money says a unit of currency today is worth more than the same unit later, because it can earn a return. You solve problems by moving cash flows to one date using FV = PV × (1 + r)^N, then matching the rate, the period and the timing of payments.

What this chapter covers

This chapter teaches you how to move cash flows across time. You start with what an interest rate is made of: a required rate of return reflects the real risk-free rate, expected inflation and premiums for risk. Then you learn to convert between stated rates and effective annual rates, and to compute future and present values of a single sum, an annuity, a perpetuity and an uneven series.

The tools are few, but they appear everywhere. Loan amortization, implied rates, growth rates and equivalence of cash flows at different dates are all applications of one idea: a value at one date equals a value at another date once you apply the right rate for the right number of periods. Most errors come from mismatched rates and periods, not from hard math.

This chapter is a base for the rest of the paper. Bond pricing and yield in Fixed Income, dividend discount models in Equities, NPV and IRR in Corporate Finance, forward pricing in Derivatives, and return measures in Quantitative Methods and Portfolio Construction all rely on discounting. If you are fast and accurate here, later topics become much easier.

Time value of money is a skill you use in many other topics, so each hour spent here pays back several times. Questions are standalone three-option items with about 90 seconds each, so you need quick, reliable keystrokes on the TI BA II Plus or HP 12C. A candidate who is slow or careless with sign conventions, compounding frequency and annuity timing loses marks here and in Fixed Income, Equities and Corporate Finance. Because there is no penalty for wrong answers, you should also learn to eliminate options by estimating: for example, a present value must be smaller than the future value for a positive rate.

The Time Value of Money in Finance: topics in the order to study them

  1. 1Interest Rates and Required Rate of ReturnIt defines what the rate r means and its components, which every later calculation uses.
  2. 2Effective Annual Rate and Compounding FrequencyYou must convert a stated rate into the correct periodic rate before you can discount or compound.
  3. 3Future Value and Present Value of a Single Cash FlowThe single-sum formula is the building block for annuities, series and applications.
  4. 4Annuities and PerpetuitiesThey extend the single-sum idea to equal repeated payments, with ordinary and due timing.
  5. 5Uneven Cash Flow Series and Loan AmortizationYou discount each flow separately, then see how a level loan payment splits into interest and principal.
  6. 6Applications: Implied Rates, Growth Rates and EquivalenceIt solves for the rate or growth instead of the value and ties everything together, so it comes last.

How to prepare The Time Value of Money in Finance

Work in short, calculator-in-hand sessions. The chapter rewards repetition more than reading, so aim for speed and accuracy.

  1. Set up your calculator first. On the TI BA II Plus, set P/Y = 1 and C/Y = 1 through 2ND P/Y, and set decimals high with 2ND FORMAT. Check the END/BGN mode before every annuity question. On the HP 12C, watch for the BEGIN indicator.
  2. Read the topics in the order above and write one formula per topic on a single page: FV = PV × (1 + r)^N, EAR = (1 + stated rate ÷ m)^m − 1, PV of a perpetuity = PMT ÷ r, and so on.
  3. For every problem, list N, I/Y, PV, PMT and FV before pressing keys. Confirm that N and I/Y use the same period length, whether annual, quarterly or monthly.
  4. Practise the sign convention: cash you pay is negative, cash you receive is positive. Clear the time value registers between problems (2ND CLR TVM on the TI; f CLEAR FIN on the HP 12C).
  5. Estimate before you calculate. Decide whether the answer should be larger or smaller than the given figure. This helps you eliminate two of the three options fast.
  6. Do mixed sets of timed questions, about 90 seconds each, and log each error by type: rate, period, timing, sign or keystroke.
  7. In the last week, redo only your logged errors and the quick revision list until you can solve each type without hesitation.

Common mistakes in The Time Value of Money in Finance

  • Using an annual rate with a monthly or quarterly number of periods

    Fix: Divide the stated rate by m and multiply the years by m, or convert to an EAR first. Write both on paper before keying.

  • Treating an annuity due as an ordinary annuity

    Fix: Check END or BGN before every annuity question. Alternatively, compute the ordinary value and multiply by (1 + r).

  • Getting the sign wrong between PV and FV or PMT

    Fix: Enter outflows as negative and inflows as positive. Reuse the same convention in every problem.

  • Confusing stated rate with effective annual rate when comparing offers

    Fix: Convert each to EAR and compare those. For a given stated rate, more frequent compounding gives a higher EAR.

  • Valuing a perpetuity or delayed annuity at the wrong date

    Fix: Find the value at the date just before the first payment, then discount it back to today as a single sum.

  • Not clearing the calculator registers

    Fix: Clear the TVM registers after every problem and re-enter every variable, including zero for any unused one.

Last-day revision: The Time Value of Money in Finance

  • Required rate of return is built from the real risk-free rate, expected inflation and risk premiums.
  • FV = PV × (1 + r)^N; PV = FV ÷ (1 + r)^N.
  • Match the rate and N to the same period: monthly rate with number of months.
  • Periodic rate = stated annual rate ÷ m, where m is compounding periods per year.
  • EAR = (1 + stated rate ÷ m)^m − 1; EAR rises as compounding becomes more frequent for a given stated rate.
  • Continuous compounding: EAR = e^(stated rate) − 1.
  • An ordinary annuity pays at the end of each period; an annuity due pays at the start, so its value is the ordinary annuity value × (1 + r).
  • Perpetuity PV = PMT ÷ r, valued one period before the first payment.
  • For uneven cash flows, discount each flow separately and add the results.
  • A level loan payment is fixed; interest falls and principal repaid rises over time.
  • Implied growth rate = (FV ÷ PV)^(1 ÷ N) − 1.
  • Two cash flows are equivalent at a given rate when they have the same value at the same date.

The Time Value of Money in Finance practice questions

The Time Value of Money in Finance in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

The Time Value of Money in Finance: frequently asked questions