Free SOA Exam FM (Financial Mathematics) General Cash Flows, Portfolios, and Asset-Liability Management Practice Questions

General cash flow analysis on SOA Exam FM integrates time value of money, annuities, and bond concepts into portfolio immunization, asset-liability management, and real-world financial decision-making scenarios.

309 questions 144 easy 106 medium 59 hard 2026 syllabus

Sample Questions

Question 1 Easy
Which of the following best describes a spot rate?
Solution
D is correct.

A spot rate sts_t is the annual effective yield on a zero-coupon investment from time 0 to time tt. It represents the rate at which a single cash flow at time tt is discounted to the present.
Question 2 Medium
Which of the following statements about convexity is NOT correct?
Solution
C is correct.

The statement that convexity is always negative for a standard fixed-coupon bond is NOT correct. Convexity for standard fixed-coupon bonds is always **positive** because the second derivative of the price with respect to yield is positive:
C=1Pd2Pdy2>0C = \frac{1}{P} \frac{d^2P}{dy^2} > 0

Positive convexity means the price-yield curve bows upward, which benefits the bondholder: prices rise more than duration predicts when yields fall, and fall less when yields rise. Negative convexity only occurs for callable bonds or mortgage-backed securities where cash flows change with interest rates.
Question 3 Hard
A 5-year bond pays annual coupons of 8% on a face value of $1,000 at an annual effective yield of 6%. Calculate the convexity of this bond.
Solution
A is correct.

Cash flows: 80 at times 1 through 4, and 1080 at time 5. Yield i=6%i = 6\%.

Compute present values:
PV1=80/1.06=75.472PV_1 = 80/1.06 = 75.472
PV2=80/1.062=71.200PV_2 = 80/1.06^2 = 71.200
PV3=80/1.063=67.170PV_3 = 80/1.06^3 = 67.170
PV4=80/1.064=63.368PV_4 = 80/1.06^4 = 63.368
PV5=1080/1.065=807.072PV_5 = 1080/1.06^5 = 807.072

Price P=1084.28P = 1084.28.

Convexity formula: C=∑t(t+1)⋅PVt(1+i)2×PC = \frac{\sum t(t+1) \cdot PV_t}{(1+i)^2 \times P}.

Compute ∑t(t+1)⋅PVt\sum t(t+1) \cdot PV_t:
1(2)(75.472)=150.941(2)(75.472) = 150.94
2(3)(71.200)=427.202(3)(71.200) = 427.20
3(4)(67.170)=806.043(4)(67.170) = 806.04
4(5)(63.368)=1267.364(5)(63.368) = 1267.36
5(6)(807.072)=24212.165(6)(807.072) = 24212.16

Sum =26863.70= 26863.70.

C=26863.70(1.06)2×1084.28=26863.701.1236×1084.28=26863.701218.30=22.05C = \frac{26863.70}{(1.06)^2 \times 1084.28} = \frac{26863.70}{1.1236 \times 1084.28} = \frac{26863.70}{1218.30} = 22.05.
Create a Free Account to Access All 309 Questions →

Browse Exam FM practice samples, free with step-by-step solutions and no signup.

Guides & Articles

Free Exam FM Sample Questions: 454 SOA-Published Items, Interactive (2026) Which Actuarial Exam Should You Take First? (2026 Order Guide) Can ChatGPT Write Good Practice Questions? The 7 Tells SOA Exam FM Study Guide: Financial Mathematics Tips for 2026

About FreeFellow

Jeffrey Ting, founder of FreeFellow
Jeffrey Ting
FSA, CFA · Founder

FreeFellow was built by Jeffrey Ting, a credentialed actuary and CFA charterholder who has passed thirteen of the hardest exams in finance, all on his first attempt. He paid four-figure prep fees along the way.

So he started writing his own questions, then lessons, then mock exams, until it grew into a full prep platform covering 40 exams with more than 45,000 original practice questions.

01
Cost shouldn't decide who gets in.

A CFA charter, a CPA license, an actuarial credential. Each opens a real career, but prep fees add to the cost of getting there. FreeFellow keeps its original question bank and written lessons free so you can study even if a paid course is out of reach.

02
Free should mean free.

The original question bank, the worked solutions, the topic lessons, mixed practice, and your readiness score stay free, forever. Full access needs a free account, and practice usage limits apply. Fellow adds AI grading on supported exams, spaced-repetition flashcards, full-length mock exams, analytics, and a study plan that adapts to your progress.

Meet the founder ›Read the values ›