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FRM Part I · FRM Exam Part I

Interest Rates for FRM Part I: Chapter Guide

Interest rates in FRM Part I cover how rates are quoted and compounded, how spot, forward and par rates link together, how bonds are priced and how their prices react to yield changes. You solve questions by picking the right formula, converting compounding first, then calculating step by step. Practise with a financial calculator.

What this chapter covers

This chapter covers the language and mathematics of interest rates. You start with how rates are quoted and compounded, then move to spot, forward and par rates, bond pricing and yield to maturity, duration and convexity, theories of the term structure, and hedging with interest rate futures.

The chapter is quantitative. Most questions give you numbers and ask for one result: a price, a yield, a forward rate, a price change or a hedge ratio. A few questions are conceptual, usually on term structure theories or why a measure has a limitation.

It connects to the rest of the paper in several ways. Compounding and discounting feed into valuation and risk models. Duration and convexity are the base for fixed income risk measures and for market risk work. Forward rates and futures link to the financial markets and products material on forwards, futures and swaps. If you master this chapter, much of the later material becomes easier.

Interest rate mathematics appears directly in questions and indirectly in many others, because pricing anything that pays cash later needs discounting. The calculations are mechanical once you know the method, so this chapter rewards practice more than most. With 100 questions in 4 hours, you need to solve these quickly and accurately. Time spent here builds speed and accuracy that carries over to bond, derivative and risk model questions.

Interest Rates: topics in the order to study them

  1. 1Types of Interest Rates and CompoundingEvery later calculation depends on converting between annual, periodic and continuous compounding correctly.
  2. 2Spot, Forward and Par RatesYou need these rate types to discount cash flows and to understand how bond prices are built from the curve.
  3. 3Bond Pricing and Yield to MaturityOnce you can discount with the right rates, you can price a bond and see yield as a single summary rate.
  4. 4Duration and ConvexityThese measure price sensitivity to yield changes, so they only make sense after you can price a bond.
  5. 5Term Structure TheoriesThis is the conceptual part. It explains the shape of the curve you have already used, and is quicker to learn after the maths.
  6. 6Interest Rate Hedging and FuturesIt applies duration and forward rates to manage risk, so it comes last.

How to prepare Interest Rates

Treat this chapter as a skills chapter. You learn the formulas once, then drill until the steps are automatic.

  1. Write one formula sheet in your own words. Include compounding conversions, continuous compounding, bond price, forward rate, duration and convexity approximations, and the hedge ratio.
  2. Learn your financial calculator for time value of money. Practise inputs for N, I/Y, PV, PMT and FV, and set payments per year correctly.
  3. For each topic, solve a few questions by hand first, then check with the calculator so you understand the method and can verify the result.
  4. Always write the compounding frequency next to a rate before you use it. Convert first, calculate second.
  5. Build a short table of how bond price, duration and convexity respond when coupon, maturity or yield changes. Use it to answer conceptual questions without calculating.
  6. Memorise the main term structure theories with one sentence each on what they say about the curve and about risk premiums.
  7. Finish with timed mixed sets. Aim for about two minutes per question, and mark the ones where you lost time to revisit the method.

Common mistakes in Interest Rates

  • Using a rate without converting its compounding frequency

    Fix: Write the frequency beside every rate. Convert to the frequency of the cash flows before discounting.

  • Treating semiannual yields as annual in bond pricing

    Fix: Divide the yield by two, double the number of periods, and halve the annual coupon for each payment.

  • Forgetting the negative sign in the duration formula

    Fix: Use ΔP ÷ P ≈ −D × Δy. A rise in yield means a fall in price.

  • Ignoring convexity when the yield change is large

    Fix: Add the convexity term when the question gives convexity or a large yield shift. It always adds to the price change.

  • Mixing up spot, forward and par rates

    Fix: Spot discounts a single cash flow, forward covers a future period, and par prices a coupon bond at par. Identify which one the question needs.

  • Taking the wrong side in a futures hedge

    Fix: Ask what loses value if rates rise. A bond holder loses, so they short futures. Then compute the size.

Last-day revision: Interest Rates

  • Compounding conversion: (1 + Rm ÷ m)^m = e^Rc, so Rc = m × ln(1 + Rm ÷ m).
  • A higher compounding frequency gives a higher effective annual rate for the same quoted rate.
  • Bond price = Σ of coupons and principal, each discounted at the right rate.
  • Yield to maturity is the single discount rate that equates the present value of cash flows to the price.
  • A bond trades at a discount when its coupon rate is below its yield, and at a premium when above.
  • Par rate is the coupon rate that prices a bond at par.
  • Forward rate between T1 and T2 with continuous compounding: (R2 × T2 − R1 × T1) ÷ (T2 − T1).
  • Modified duration ≈ Macaulay duration ÷ (1 + y ÷ m).
  • Price change ≈ −D × Δy + ½ × C × (Δy)², using modified duration D and convexity C.
  • Convexity helps the holder: price gains from a yield fall exceed losses from an equal yield rise.
  • Expectations theory sees forward rates as expected future spot rates; liquidity preference adds a premium for longer maturities.
  • Hedge with futures using a ratio based on the portfolio and futures durations and values, and check the sign of the position.

Interest Rates practice questions

Interest Rates in other exams

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

Interest Rates: frequently asked questions

How much of FRM Part I is about interest rates?

GARP does not publish a fixed mark allocation for individual chapters in the form of a pass mark. Interest rate ideas run across several topics, so treat this chapter as a core skill. Check the current GARP Study Guide for the readings assigned to you.

Do I need a financial calculator for this chapter?

It helps a lot for bond price, yield to maturity and time value questions. Learn it before you practise, and also be able to do simple cases by hand to check your answers. Confirm the permitted calculators on GARP's site before exam day.

Which topic in this chapter should I master first?

Start with compounding. Errors in compounding conversion carry into forwards, bond prices and yields, so it is the most valuable foundation.

How are duration and convexity tested?

Expect questions that estimate a price change from a yield change, compare bonds by duration, and ask how coupon, maturity or yield affects convexity. Practise both the calculation and the concept.