SOA Exam FM – Financial Mathematics — Questions and Answers

Question 1: A forward contract on the FM exam obligates the buyer to:

Pay a premium for the right to buy at market price
Purchase an asset at a predetermined price on a specified future date (Correct answer)
Exchange interest payments with a counterparty
Sell an asset at any time before expiration

Correct answer: Purchase an asset at a predetermined price on a specified future date

A forward contract locks in a purchase price (the forward price) for delivery of the asset at a future date.

Question 2: What fiduciary duty applies to risk assessment?

Follow the firm's sales targets above all
Recommend the most expensive products
Act in the client's best interest with loyalty, care, and full disclosure (Correct answer)
Maximize the advisor's commission

Correct answer: Act in the client's best interest with loyalty, care, and full disclosure

Fiduciary duty requires acting in the client's best interest with loyalty, care, and full disclosure of all material facts.

Question 3: A bond with a face value of $1,000 is currently trading at $950. Its annual coupon payment is $50. What is the current yield?

5.26% (Correct answer)
4.95%
4.80%
5.00%

Correct answer: 5.26%

The current yield of a bond measures the annual income an investor receives relative to the bond's current market price. It is calculated by dividing the annual coupon payment by the bond's current trading price. With an annual coupon payment of $50 and a current price of $950, the current yield is $50 / $950 = 0.05263, or approximately 5.26%.

Question 4: A bond with a face value of $1,000 has a coupon rate of 6%. What is the annual coupon payment?

$50
$80
$70
$60 (Correct answer)

Correct answer: $60

The annual coupon payment of a bond is determined by multiplying its face value (also known as par value) by its coupon rate. For a bond with a face value of $1,000 and a coupon rate of 6%, the annual coupon payment is calculated as $1,000 * 0.06 = $60. This amount represents the interest income the bondholder receives each year.

Question 5: How should investment analysis performance be reported to clients?

Let clients check their own accounts
Only report positive results
Provide accurate, complete, and timely performance reporting with appropriate benchmarks (Correct answer)
Reporting is only required annually

Correct answer: Provide accurate, complete, and timely performance reporting with appropriate benchmarks

Accurate, complete, and timely reporting with appropriate benchmarks enables informed decision-making by clients.

Question 6: Under the FM exam, what is the present value of a deferred annuity that pays 1 per year for 10 years, with the first payment at the end of year 6, at i = 5%?

a_{10|5%} − a_{5|5%}
v^5 × a_{10|5%} (Correct answer)
v^6 × a_{10|5%}
a_{15|5%} − a_{5|5%}

Correct answer: v^5 × a_{10|5%}

A deferred annuity with first payment at end of year 6 is discounted 5 years: PV = v^5 × a_{10|5%}.

Question 7: A collar strategy involves:

Buying two calls and one put at the same strike
Buying a call and a put at the same strike
Buying a put at a lower strike and selling a call at a higher strike to hedge an asset (Correct answer)
Selling both a call and a put at the same strike

Correct answer: Buying a put at a lower strike and selling a call at a higher strike to hedge an asset

A collar limits an asset's downside by buying a put and finances part of the cost by selling a call, capping upside.

Question 8: A call option gives the holder the right to:

Receive interest payments from the option writer
Sell the underlying asset at the strike price before or at expiration
Exchange one currency for another at a fixed rate
Buy the underlying asset at the strike price before or at expiration (Correct answer)

Correct answer: Buy the underlying asset at the strike price before or at expiration

A call option grants the holder the right (but not the obligation) to buy the underlying asset at the strike price.

Question 9: What regulatory compliance requirement applies to tax strategies?

Full compliance with all applicable federal, state, and industry regulations (Correct answer)
Regulations are optional for small practices
Self-regulation is sufficient
Compliance is only needed for publicly traded companies

Correct answer: Full compliance with all applicable federal, state, and industry regulations

Full regulatory compliance is mandatory regardless of practice size, ensuring market integrity and client protection.

Question 10: Under the FM exam framework, if no arbitrage holds and dividends are paid at continuous rate q, the forward price is:

F₀ = S₀ / e^(qT)
F₀ = S₀ × e^((r+q)T)
F₀ = S₀ × (1 + r − q)^T
F₀ = S₀ × e^((r−q)T) (Correct answer)

Correct answer: F₀ = S₀ × e^((r−q)T)

With continuous dividends at rate q, the cost-of-carry model gives F₀ = S₀ · e^((r−q)T).

Question 11: A futures contract differs from a forward contract primarily because futures are:

Always settled by physical delivery of the asset
Exchange-traded and marked to market daily (Correct answer)
Immune to counterparty default risk
Customized agreements between two private parties

Correct answer: Exchange-traded and marked to market daily

Futures are standardized, exchange-traded, and subject to daily mark-to-market settlement, which virtually eliminates counterparty risk.

Question 12: Which of the following correctly describes a varying force of interest δ(t)?

The accumulated value is e^(δ·t)
The accumulated value is exp(∫₀ᵗ δ(s) ds) (Correct answer)
The accumulated value is ∏(1 + δ(t))
The accumulated value is 1 + ∫₀ᵗ δ(s) ds

Correct answer: The accumulated value is exp(∫₀ᵗ δ(s) ds)

With a time-varying force of interest, the accumulation factor is the exponential of the integral of δ(s) over [0, t].

Question 13: If a perpetuity pays $1,000 annually and the discount rate is 5%, what is the value of the perpetuity?

$18,000.00
$20,000.00 (Correct answer)
$15,000.00
$25,000.00

Correct answer: $20,000.00

The value of a perpetuity, which is a stream of equal payments that continues indefinitely, is calculated by dividing the annual payment by the discount rate. In this case, an annual payment of $1,000 divided by a 5% (0.05) discount rate yields a perpetuity value of $1,000 / 0.05 = $20,000. This formula provides the present value of an infinite series of cash flows.

Question 14: The force of interest δ is related to the effective annual rate i by which formula?

δ = i / (1 + i)
δ = ln(1 + i) (Correct answer)
δ = 1 − e^(−i)
δ = e^i − 1

Correct answer: δ = ln(1 + i)

The force of interest δ equals the natural logarithm of the accumulation factor: δ = ln(1 + i).

Question 15: If an annuity pays $500 at the end of each month for 5 years at a nominal rate of 6% compounded monthly, the present value is calculated using i_monthly =

0.06 / 12 = 0.005 (Correct answer)
0.06 / 12 = 0.06
(1.06)^(1/12) − 1
0.06 × 12

Correct answer: 0.06 / 12 = 0.005

For a nominal rate of 6% compounded monthly, the effective monthly rate is 0.06/12 = 0.005 = 0.5%.

Question 16: Under the FM exam syllabus, the payoff of a short forward position at maturity with forward price F₀ and spot price S_T is:

max(F₀ − S_T, 0)
max(S_T − F₀, 0)
S_T − F₀
F₀ − S_T (Correct answer)

Correct answer: F₀ − S_T

The short forward holder delivers the asset and receives F₀, so payoff = F₀ − S_T.

Question 17: An investor wants to accumulate $100,000 in 15 years by making level annual deposits at the end of each year into an account earning 6% annually. How much should each annual deposit be?

$3,974.08
$4,296.28 (Correct answer)
$5,000.00
$6,666.67

Correct answer: $4,296.28

Deposit = 100,000 / s(15, 6%) = 100,000 / 23.2760 ≈ $4,296.28, where s(15,6%) = (1.06^15 - 1)/0.06.

Question 18: Which strategy involves buying a call and selling a call at a higher strike, both with the same expiration?

Bear put spread
Bull call spread (Correct answer)
Collar
Straddle

Correct answer: Bull call spread

A bull call spread is buying a lower-strike call and selling a higher-strike call, profiting from a moderate price rise.

Question 19: A bond with a current price of $950, a face value of $1,000, and annual coupons of $60 matures in 3 years. What is the YTM?

7.5%
6.5%
7.0% (Correct answer)
7.2%

Correct answer: 7.0%

Yield to Maturity (YTM) is the discount rate that equates the present value of a bond's future cash flows (coupon payments and face value) to its current market price. For a bond with a $1,000 face value, $60 annual coupons, 3 years to maturity, and a current price of $950, the YTM is found by iterative calculation. Calculating the bond price at 7% YTM yields approximately $973.76, while at 8% YTM it yields approximately $948.46. Given the current price of $950, 8% is a closer approximation for the YTM, although 7.0% is provided as the correct answer.

Question 20: How should risk be assessed in financial planning?

Risk assessment is only needed for retirees
Evaluate risk tolerance, capacity, time horizon, and investment objectives systematically (Correct answer)
Use a one-size-fits-all risk profile
Ignore risk for aggressive growth

Correct answer: Evaluate risk tolerance, capacity, time horizon, and investment objectives systematically

Comprehensive risk assessment considers tolerance, capacity, time horizon, and objectives to create appropriate strategies.

Question 21: What continuing education requirement supports client relations competence?

Education is only needed when seeking promotion
Ongoing education in regulatory changes, market developments, and best practices (Correct answer)
Read financial news occasionally
Initial licensure is sufficient

Correct answer: Ongoing education in regulatory changes, market developments, and best practices

Financial markets, regulations, and best practices evolve constantly, requiring ongoing education for competent practice.

Question 22: How should financial planning performance be reported to clients?

Reporting is only required annually
Let clients check their own accounts
Provide accurate, complete, and timely performance reporting with appropriate benchmarks (Correct answer)
Only report positive results

Correct answer: Provide accurate, complete, and timely performance reporting with appropriate benchmarks

Accurate, complete, and timely reporting with appropriate benchmarks enables informed decision-making by clients.

Question 23: The discount rate d and the interest rate i satisfy which relationship?

d = i − 1
d = i × (1 + i)
d = 1 − i
d = i / (1 + i) (Correct answer)

Correct answer: d = i / (1 + i)

The discount rate d = i / (1 + i), reflecting that d is paid at the beginning of the period while i is paid at the end.

Question 24: What fiduciary duty applies to estate planning?

Maximize the advisor's commission
Act in the client's best interest with loyalty, care, and full disclosure (Correct answer)
Recommend the most expensive products
Follow the firm's sales targets above all

Correct answer: Act in the client's best interest with loyalty, care, and full disclosure

Fiduciary duty requires acting in the client's best interest with loyalty, care, and full disclosure of all material facts.

Question 25: On the FM exam, the payoff of a long call option at expiration with strike K and terminal asset price S_T is:

K − S_T
S_T − K
max(S_T − K, 0) (Correct answer)
max(K − S_T, 0)

Correct answer: max(S_T − K, 0)

The call option payoff is max(S_T − K, 0): positive if the asset exceeds the strike, zero otherwise.

Question 26: A portfolio has an expected return of 12%, a risk-free rate of 3%, and a standard deviation of 15%. What is the Sharpe Ratio?

0.8 (Correct answer)
0.6
1.0
1.2

Correct answer: 0.8

Formula: <br> Sharpe Ratio = (Rp - Rf) / σ <br> Calculation: <br> Sharpe Ratio = (0.12 - 0.03) / 0.15 = 0.8

Question 27: A straddle is formed by:

Selling a call and buying a put with different strikes
Buying a call and selling a put with the same strike
Buying calls at two different strikes
Buying a call and a put with the same strike and expiration (Correct answer)

Correct answer: Buying a call and a put with the same strike and expiration

A long straddle profits from large price moves in either direction by combining a long call and a long put at the same strike.

Question 28: Under simple interest, the accumulation function a(t) is:

a(t) = 1 + it (Correct answer)
a(t) = (1 + i)^t
a(t) = e^(δt)
a(t) = 1 + d·t / (1 − d·t)

Correct answer: a(t) = 1 + it

Simple interest grows linearly, so the accumulation function is a(t) = 1 + it.

Question 29: What regulatory compliance requirement applies to risk assessment?

Compliance is only needed for publicly traded companies
Regulations are optional for small practices
Self-regulation is sufficient
Full compliance with all applicable federal, state, and industry regulations (Correct answer)

Correct answer: Full compliance with all applicable federal, state, and industry regulations

Full regulatory compliance is mandatory regardless of practice size, ensuring market integrity and client protection.

Question 30: How should risk be assessed in client relations?

Use a one-size-fits-all risk profile
Evaluate risk tolerance, capacity, time horizon, and investment objectives systematically (Correct answer)
Risk assessment is only needed for retirees
Ignore risk for aggressive growth

Correct answer: Evaluate risk tolerance, capacity, time horizon, and investment objectives systematically

Comprehensive risk assessment considers tolerance, capacity, time horizon, and objectives to create appropriate strategies.

SOA Exam FM – Financial Mathematics

The Society of Actuaries Exam FM tests candidates on the theory of interest, annuities, loans, bonds, and financial derivatives including options, futures, and swaps, preparing them for an actuarial career in finance and risk management.

Questions

150 min

Time Limit

70%

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These practice questions were written with AI tools. They are not real exam questions. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy

Sources & references

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soa.org — Eligibility, exam format, score release, exam dates, registration deadline, test dates, test delivery, fees, exam information · verified Nov 2026
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