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A deposit of 1,000 is invested at 6% annual effective interest. What is the accumulated value at the end of 3 years?

1,175.00

1,191.02

1,236.00

1,240.00

to track

2026 Statistics

Key Facts: SOA FM Exam

Official Questions

SOA April 2026 syllabus

2.5 hrs

Time Limit

SOA

6-10

Passing Grades

SOA 0-10 scale

$275

Standard Fee

SOA fee table

Content Domains

SOA syllabus

200

Practice Questions Here

OpenExamPrep

SOA FM is a 30-question preliminary actuarial exam administered in 2.5 hours. The April 2026 syllabus uses five weighted domains, with the heaviest emphasis on annuities and loans plus derivatives and risk management. SOA reports grades on a 0-10 scale, and a grade of 6 or higher is passing. As of March 11, 2026, the official FM updates page listed no content updates.

Sample SOA FM Practice Questions

Try these sample questions to test your SOA FM exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 200+ question experience with AI tutoring.

1A deposit of 1,000 is invested at 6% annual effective interest. What is the accumulated value at the end of 3 years?

A.1,175.00

B.1,191.02

C.1,236.00

D.1,240.00

Explanation: Use compound accumulation: 1000(1.06)^3 = 1191.016. Annual effective interest compounds once per year, so the accumulated value rounds to 1,191.02.

2A nominal discount rate of 8% convertible quarterly is given. What is the equivalent annual effective interest rate?

A.7.92%

B.8.16%

C.8.42%

D.8.67%

Explanation: For a nominal discount rate d^(4) = 0.08, each quarter has discount 0.02, so the quarterly accumulation factor is 1 / (1 - 0.02). The annual effective interest rate is (1 / 0.98)^4 - 1 = 0.08417, or about 8.42%.

3An account earns 5% annual effective for 2 years and 6% annual effective for the next 3 years. What single annual effective rate is equivalent over the full 5-year period?

A.5.40%

B.5.60%

C.5.80%

D.6.00%

Explanation: Set (1 + i)^5 = 1.05^2 x 1.06^3. Solving gives i = (1.05^2 x 1.06^3)^(1/5) - 1 = 0.05599, so the equivalent annual effective rate is about 5.60%.

4For 0 <= t <= 2, the force of interest is delta_t = 0.04 + 0.01t. What is the accumulated value at time 2 of 1,000 invested at time 0?

A.1,083.29

B.1,105.17

C.1,127.50

D.1,140.00

Explanation: With a varying force, the accumulation factor is exp(integral from 0 to 2 of (0.04 + 0.01t) dt). The integral is 0.04(2) + 0.01(2^2)/2 = 0.10, so the value is 1000e^0.10 = 1,105.17.

5The annual effective discount rate is 7%. What is the equivalent annual effective interest rate?

A.6.54%

B.7.00%

C.7.53%

D.8.12%

Explanation: Annual effective interest and discount satisfy i = d / (1 - d). Substituting d = 0.07 gives i = 0.07 / 0.93 = 0.07527, or 7.53%.

6What is the present value of an annuity-immediate paying 1,000 at the end of each year for 5 years, assuming 5% annual effective interest?

A.4,250.00

B.4,329.48

C.4,500.00

D.5,000.00

Explanation: For an annuity-immediate, PV = 1000 a-angle-5 at 5%. That is 1000[(1 - 1.05^-5)/0.05] = 4,329.48.

7An annuity-due pays 500 monthly for 2 years. If the nominal annual interest rate is 6% convertible monthly, what is the accumulated value at the end of 2 years?

A.12,632.00

B.12,715.98

C.12,779.56

D.12,843.46

Explanation: The monthly rate is 0.06 / 12 = 0.005. The accumulated value of the annuity-due is 500 s-angle-24 at 0.5% per month times 1.005, which gives 12,779.56.

8A perpetuity-immediate pays 80 at the end of each quarter forever. If the annual effective interest rate is 8%, what is the present value?

A.4,000.00

B.4,118.08

C.4,201.71

D.4,320.00

Explanation: Convert the annual effective rate to an effective quarterly rate: j = 1.08^(1/4) - 1. The present value of a perpetuity-immediate is 80 / j = 4,118.08.

9A loan of 10,000 is repaid by level annual payments for 4 years at 6% annual effective interest. What is the annual payment?

A.2,720.15

B.2,885.91

C.2,967.20

D.3,154.00

Explanation: For a fully amortized loan, payment = 10000 / a-angle-4 at 6%. This gives 10000 / 3.46511 = 2,885.91.

10A 20,000 loan is amortized by level annual payments over 10 years at 5% annual effective interest. What is the outstanding balance immediately after the 5th payment?

A.10,950.37

B.11,213.74

C.11,459.12

D.11,795.54

Explanation: First find the level payment: 20000 / a-angle-10 at 5% = 2,590.09. Immediately after the 5th payment, 5 payments remain, so the outstanding balance is 2,590.09 a-angle-5 at 5% = 11,213.74.

About the SOA FM Exam

The SOA Financial Mathematics (FM) exam is a core preliminary actuarial exam covering interest theory, annuities, loans, bonds, cash-flow analysis, derivatives, and risk management.

Assessment

30 multiple-choice questions

Time Limit

2 hours 30 minutes

Passing Score

Grade of 6 or higher on SOA's 0-10 scale

Exam Fee

$275 (Society of Actuaries (SOA) / Prometric)

SOA FM Exam Content Outline

5-15%

Interest Theory

Accumulation, discounting, force of interest, and equivalent rate relationships.

20-30%

Annuities and Loans

Level and varying annuities, amortization, sinking funds, and loan balance mechanics.

15-25%

Bonds

Bond price-yield relationships, premium and discount amortization, and fixed-income valuation.

15-25%

General Cash Flows and Portfolios

Net present value, internal rate of return, project comparison, duration, and portfolio matching.

20-30%

Derivatives and Risk Management

Forwards, futures, swaps, options, hedging logic, and no-arbitrage pricing intuition.

How to Pass the SOA FM Exam

What You Need to Know

Passing score: Grade of 6 or higher on SOA's 0-10 scale
Assessment: 30 multiple-choice questions
Time limit: 2 hours 30 minutes
Exam fee: $275

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

SOA FM Study Tips from Top Performers

1Master interest-rate conversion mechanics first so nominal, effective, discount, and force-of-interest questions become setup exercises instead of memory tests.

2Spend extra time on annuity and loan identities because they are both high-weighted and foundational for several other FM question types.

3Practice bond problems with premium, discount, and yield language until you can move quickly between book value, price, and amortization interpretations.

4Treat duration and immunization as concept-plus-computation topics: know the formulas, but also know what a hedge or matched portfolio is trying to accomplish.

5For derivatives, focus on payoff structure, no-arbitrage forward pricing, and whether a position is long or short before you start calculating.

Frequently Asked Questions

How many questions are on SOA Exam FM?

The April 2026 SOA FM syllabus lists 30 multiple-choice questions. That is the current official format for 2026 sittings.

How long is the SOA FM exam?

You get 2 hours and 30 minutes to complete FM. Because the exam is calculation-heavy, pacing matters almost as much as formula recall.

What is the passing score for SOA FM?

SOA reports preliminary exam grades on a 0-10 scale, and grades from 6 to 10 are passing. The SOA does not publish a fixed raw percentage because the pass mark is set for each sitting.

Which topics matter most on FM?

The current blueprint puts the most weight on Annuities and Loans plus Derivatives and Risk Management at 20-30% each. Bonds and General Cash Flows and Portfolios are mid-weight at 15-25% each, while Interest Theory is smaller at 5-15%.

What changed for SOA FM in 2026?

As of March 11, 2026, the official FM updates page says there are currently no content updates. The practical 2026 changes students should notice are the current $275 exam fee and SOA's January 2026 outreach about expanding on-campus testing opportunities for future administrations.

How much does SOA FM cost?

The listed 2026 standard exam fee for FM is $275. Registration is handled through SOA with Prometric scheduling for computer-based administrations.