Are you preparing for the Society of Actuaries (SOA) Exam FM? This comprehensive cheat sheet covers all the essential financial mathematics concepts you need to master. Use this as your quick reference guide while studying!
Contents
Key Information About Exam FM
The SOA Exam FM tests your knowledge of financial mathematics concepts. Here’s what you need to know:
- Duration: 3 hours
- Number of questions: 30 multiple-choice questions
- Passing score: Typically around 70% (varies by sitting)
- Calculator: Only BA-II Plus or BA-II Plus Professional allowed
Time Value of Money
Basic Interest Rates
Simple Interest:
- Accumulated Value: A = P(1 + rt)
- Where: P = Principal, r = interest rate, t = time
Compound Interest:
- Accumulated Value: A = P(1 + i)^n
- Where: i = interest rate per period, n = number of periods
Effective Interest Rate:
- i = (1 + r/n)^n – 1
- Where: r = nominal rate, n = number of compounding periods per year
Present and Future Values
Present Value:
- PV = FV × (1 + i)^(-n)
Future Value:
- FV = PV × (1 + i)^n
Annuities
Ordinary Annuity (payments at end of period):
- Present Value: PV = PMT × [(1 – (1 + i)^(-n))/i]
- Future Value: FV = PMT × [((1 + i)^n – 1)/i]
Annuity Due (payments at start of period):
- Present Value: PV = PMT × [(1 – (1 + i)^(-n))/i] × (1 + i)
- Future Value: FV = PMT × [((1 + i)^n – 1)/i] × (1 + i)
Perpetuities
Present Value of Perpetuity:
- PV = PMT/i
- Where: PMT = payment amount, i = interest rate per period
Loans and Bonds
Loan Amortization
Payment Formula:
- PMT = PV × [i × (1 + i)^n]/[(1 + i)^n – 1]
Outstanding Balance:
- Balance after k payments = PV × (1 + i)^k – PMT × [((1 + i)^k – 1)/i]
Bonds
Bond Price Formula:
- P = r × [1 – (1 + i)^(-n)]/i + F × (1 + i)^(-n)
- Where: r = coupon payment, F = face value, n = number of periods, i = yield rate
Bond Characteristics:
- Premium Bond: Price > Face Value
- Discount Bond: Price < Face Value
- Par Bond: Price = Face Value
Financial Instruments
Stocks
Dividend Discount Model:
- P = D/(r – g)
- Where: D = next dividend, r = required return, g = growth rate
Duration and Convexity
Macaulay Duration:
- D = Σ[t × PV(CFt)]/Price
- Where: CFt = cash flow at time t
Modified Duration:
- D_mod = D/(1 + i)
Convexity:
- C = Σ[t × (t + 1) × PV(CFt)]/(Price × (1 + i)^2)
Yield Curves and Forward Rates
Spot Rates
- (1 + s_n)^n = [(1 + f_1) × (1 + f_2) × … × (1 + f_n)]
Forward Rates
- (1 + f_(t,t+1)) = (1 + s_(t+1))^(t+1)/(1 + s_t)^t
Investment Portfolio Fundamentals
Net Present Value (NPV)
NPV = -Initial Investment + Σ[CFt/(1 + r)^t]
Internal Rate of Return (IRR)
0 = -Initial Investment + Σ[CFt/(1 + IRR)^t]
Study Tips
- Master Your Calculator
- Learn all financial functions on BA-II Plus
- Practice using TVM keys efficiently
- Know how to set payment settings (BGN/END)
- Focus on Core Concepts
- Understand the relationship between interest rates
- Master present value and future value calculations
- Practice bond pricing under different scenarios
- Know how to amortize loans
- Common Pitfalls to Avoid
- Double-check payment timing (beginning vs. end)
- Verify period frequency matches interest rate
- Confirm calculator settings between problems
- Watch for changes in compounding frequency
Exam Day Strategies
- Time Management
- Spend maximum 6 minutes per question
- Skip difficult questions and return later
- Leave time to check your work
- Calculator Preparation
- Clear memory before exam
- Check battery level
- Bring backup calculator
- Verify settings (P/Y, C/Y, PMT settings)
- Quick Checks
- Does your answer make logical sense?
- Have you used consistent time periods?
- Are your decimal places correct?
- Did you consider the timing of all cash flows?
Exam Day Essentials
- Required Items:
- Valid ID
- Admission ticket
- Approved calculator
- Backup calculator
- Pre-Exam Routine:
- Arrive 30 minutes early
- Review calculator settings
- Take a few deep breaths
- Use restroom before exam starts
Final Tips
- Practice Extensively:
- Work through sample problems
- Time yourself regularly
- Review mistakes thoroughly
- Create formula flash cards
- Stay Organized:
- Write out all given information
- Draw timelines for complex problems
- Show all calculations
- Double-check your work
Remember that success in Exam FM comes from understanding the underlying concepts, not just memorizing formulas. Use this cheat sheet as a quick reference while ensuring you comprehend the fundamental principles of financial mathematics.
Good luck with your exam preparation!
