Free SOA Exam FM (Financial Mathematics) Time Value of Money Practice Questions

Time value of money is the foundational topic on SOA Exam FM, covering interest rate conversions, present and future value calculations, discount factors, and force of interest. The SOA syllabus allocates 10-15% of Exam FM to interest theory fundamentals (SOA).

145 questions 62 easy 56 medium 27 hard 2026 syllabus

Sample Questions

Question 1 Easy
Calculate the present value of $50,000 due in 12 years at an effective annual interest rate of 3%.
Solution
C is correct.

The present value is:

PV=FV⋅vn=FV(1+i)n=50,000(1.03)12PV = FV \cdot v^n = \frac{FV}{(1+i)^n} = \frac{50{,}000}{(1.03)^{12}}

Compute (1.03)12(1.03)^{12} by repeated squaring:

(1.03)2=1.0609(1.03)^2 = 1.0609

(1.03)4=(1.0609)2=1.12550881(1.03)^4 = (1.0609)^2 = 1.12550881

(1.03)8=(1.12550881)2=1.26677008(1.03)^8 = (1.12550881)^2 = 1.26677008

(1.03)12=(1.03)8×(1.03)4=1.26677008×1.12550881=1.42576089(1.03)^{12} = (1.03)^8 \times (1.03)^4 = 1.26677008 \times 1.12550881 = 1.42576089

PV=50,0001.42576089=35,069PV = \frac{50{,}000}{1.42576089} = 35{,}069

The present value is $35,069.
Question 2 Medium
A nominal interest rate of 6% compounded semiannually is given. Determine the equivalent force of interest δ\delta.
Solution
A is correct.

Step 1: Find the effective annual interest rate.

1+i=(1+0.062)2=(1.03)2=1.06091 + i = \left(1 + \frac{0.06}{2}\right)^2 = (1.03)^2 = 1.0609

Step 2: Find the force of interest.

δ=ln⁡(1+i)=ln⁡(1.0609)\delta = \ln(1 + i) = \ln(1.0609)

Alternatively: δ=2ln⁡(1.03)=2×0.029559=0.059118\delta = 2\ln(1.03) = 2 \times 0.029559 = 0.059118.

So δ≈0.05912\delta \approx 0.05912.
Question 3 Hard
Given i(4)=10%i^{(4)} = 10\%, calculate d(6)d^{(6)}.
Solution
E is correct.

Convert i(4)i^{(4)} to the force of interest δ\delta.

δ=4ln⁡(1+i(4)4)=4ln⁡(1.025)=4×0.024693=0.098771\delta = 4 \ln\left(1 + \frac{i^{(4)}}{4}\right) = 4 \ln(1.025) = 4 \times 0.024693 = 0.098771

Convert δ\delta to d(6)d^{(6)}:
d(6)=6(1−e−δ/6)=6(1−e−0.016462)d^{(6)} = 6\left(1 - e^{-\delta/6}\right) = 6\left(1 - e^{-0.016462}\right)

e−0.016462=0.98367e^{-0.016462} = 0.98367
d(6)=6×0.01633=0.09796≈9.80%d^{(6)} = 6 \times 0.01633 = 0.09796 \approx 9.80\%
Create a Free Account to Access All 145 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 ›