CFA Level I Exam · The Time Value of Money in Finance

Interest Rates and Required Rate of Return for CFA Level 1

Updated 7 October 2026 · Fact-checked

An interest rate is the required rate of return on an investment, the discount rate used to value future cash flows, and the opportunity cost of spending now. It equals the real risk-free rate plus inflation, default, liquidity and maturity premiums. You solve questions by adding the right premiums and matching them to the security's risks.

Understand Interest Rates and Required Rate of Return

An interest rate is a price. It is what a borrower pays, and what a lender must receive, for using money over time. You can read the same number in three ways.

As a required rate of return, it is the minimum return an investor needs to accept an investment. As a discount rate, it converts a future cash flow into today's value. As an opportunity cost, it is the return you give up by choosing one use of money over the next best one. If you hold cash instead of a deposit paying 4%, you give up 4%.

Now split the rate into parts. The real risk-free rate is the return for giving up consumption today when there is no inflation and no risk. The nominal risk-free rate adds expected inflation. It is roughly the rate on a short-term government bill in a stable economy, such as US Treasury bills.

Risky securities add premiums on top. The default risk premium pays for the chance the borrower fails to pay in full and on time. The liquidity premium pays for the risk of selling quickly at a price below fair value. The maturity premium pays for the higher price sensitivity of longer-term securities to interest rate changes.

So the nominal rate on a risky security is the sum of these parts. Exams test whether you know which premium applies. A government bill has no default or liquidity premium and a tiny maturity premium. A thinly traded 10-year corporate bond has all of them.

Key formulas to remember

Nominal risk-free rate: Nominal risk-free rate ≈ real risk-free rate + expected inflation premium; The curriculum uses this additive form. The exact link is the Fisher relation, (1 + nominal) = (1 + real) × (1 + inflation), which gives a slightly different value.
Required rate of return on a security: Required rate = real risk-free rate + inflation premium + default risk premium + liquidity premium + maturity premium; Drop any premium that does not apply to the security. A default-free, liquid, short-term bill has none of the three risk premiums to speak of.
Exact Fisher relation: (1 + nominal rate) = (1 + real rate) × (1 + expected inflation); Use it only when the question asks for an exact or compounded relationship. Otherwise add the rates.
Opportunity cost: Opportunity cost = return on the best alternative forgone; The discount rate for a project is the return available on alternatives of equal risk.

How to solve Interest Rates and Required Rate of Return questions

Use this method for any question on interest rate components or required return.

1Identify what is being asked: nominal rate, real rate, one premium, or a required return.
2List the components given in the stem and convert percentages to the same form (for example, 0.5% as 0.005 if you compute).
3Decide whether the question wants the simple additive form or the exact Fisher relation. Use additive unless the stem says exact or compounded.
4Match each premium to the security: default for credit risk, liquidity for ease of selling, maturity for term, inflation for lost purchasing power.
5Add the relevant premiums, or subtract the known ones to find the missing premium.
6Check the result is sensible: a riskier, longer or less liquid security should not have a lower rate than a safer one.
7Eliminate any options that fail the check, then choose the one that matches your number.

Quickest way: Add and subtract the premiums

When to use it: Use it when the stem lists premiums or gives two bond yields and asks for the difference to be explained.

Write the rate as a sum of labelled parts in the margin of your scratch paper.
Subtract the safer security's yield from the riskier one to isolate the extra premium.
Ask which risk differs between the two securities and name that premium.
Pick the option whose label and size match.

Common mistakes in Interest Rates and Required Rate of Return

Treating the nominal risk-free rate as the real risk-free rate.
Government bill yields are called risk-free, so students forget they already include inflation.
Fix: Real risk-free rate has no inflation. Nominal risk-free equals real plus inflation premium.
Assigning the liquidity premium to credit risk.
Both premiums are higher for weaker issuers, so they blur together.
Fix: Default premium is about the chance of non-payment. Liquidity premium is about difficulty of selling at fair value.
Adding a default premium to a government bill in a stable economy.
Students apply the full list mechanically.
Fix: Ask which risks the security actually carries before adding any premium.
Confusing the maturity premium with the inflation premium.
Both can be larger for longer terms, so they seem to be the same thing.
Fix: The maturity premium compensates for the greater interest rate (price) risk of longer-term securities. The inflation premium compensates for the expected loss of purchasing power.
Using the Fisher exact formula when additive is intended, or the reverse.
Students do not read whether the stem says approximate or exact.
Fix: Default to addition. Use multiplication only when the question asks for the exact relationship.

Worked examples

Example 1

The real risk-free rate is 1.5% and expected inflation is 2.0%. A corporate bond has a default risk premium of 1.2%, a liquidity premium of 0.6% and a maturity premium of 0.4%. What is the bond's required rate of return using the additive approach? Options: A) 3.5%, B) 5.3%, C) 5.7%.

Show the solution

Nominal risk-free rate = 1.5% + 2.0% = 3.5%.
Add the default premium: 3.5% + 1.2% = 4.7%.
Add the liquidity premium: 4.7% + 0.6% = 5.3%.
Add the maturity premium: 5.3% + 0.4% = 5.7%.
Option A ignores all risk premiums. Option B omits the maturity premium. Option C includes every premium and matches.

Answer: C) 5.7%

Example 2

Two bonds from the same issuer have the same maturity and credit risk. Bond X trades often. Bond Y trades rarely and yields 0.35% more. What does the extra 0.35% mainly compensate for? Options: A) Default risk, B) Liquidity risk, C) Inflation risk.

Show the solution

Same issuer and credit risk means the default premium is equal.
Same maturity means the maturity premium is equal.
Inflation expectations apply equally to both bonds.
The only difference is how easily each trades, which is liquidity.
So the extra yield is the liquidity premium.

Answer: B) Liquidity risk

Exam tips

Questions are three-option and standalone. Often you can eliminate two options by asking which risk the security actually carries.
Read for the words approximate versus exact. They decide between adding and the Fisher relation.
When two bonds are compared, find the one feature that differs and name the premium tied to it.
Keep percentages in one form. Mixing 1.5% and 0.015 causes careless errors.

Practice questions from The Time Value of Money in Finance

Interest Rates and Required Rate of Return 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 and Required Rate of Return: frequently asked questions

What is the difference between nominal and real interest rate?

The nominal rate is the quoted rate and includes compensation for expected inflation. The real rate removes inflation and shows the gain in purchasing power. Nominal is roughly real plus expected inflation.

What is opportunity cost as a discount rate?

It is the return you could earn on the best alternative investment of similar risk. You use it to discount future cash flows because investing here means giving up that alternative.

Which premiums apply to a government bill?

A short-term bill from a stable government carries mainly the real risk-free rate and an inflation premium. Default, liquidity and maturity premiums are negligible. Longer government bonds add a maturity premium.

Do I use the additive or exact formula in the exam?

Use addition unless the question asks for an exact or compounded relationship. Then use (1 + nominal) = (1 + real) × (1 + inflation).