SOA Financial Mathematics Examination Practice Test
The SOA Financial Mathematics Examination (FM) practice page covers time value of money and the mathematical analysis of cash flows. Sample problems involve present and accumulated values, effective interest and discount rates, force of interest, annuities, perpetuities, and bond pricing. These calculations connect interest-rate assumptions to the value of payments made at different times.
Exam overview
About the SOA Financial Mathematics Examination Exam
Financial mathematics requires translating a payment schedule into a consistent valuation equation. You may need to discount future receipts to find present value, accumulate deposits to a later date, or solve for an unknown yield that equates a purchase price with a stream of payments. Bond problems combine coupon cash flows and redemption value; comparing coupon rate with yield helps explain whether a bond trades at par, a premium, or a discount. Other calculations distinguish effective interest from effective discount and use a time-varying force of interest to obtain an accumulation factor. Annuity and perpetuity problems test how payment timing and frequency affect value, while continuous income requires integration or an equivalent continuous-payment valuation. Careful timeline setup, consistent rate periods, and accurate algebra help prevent sign and timing errors.
Sample Practice Questions
Review a selection from this exam's published US Practice Tests practice bank.
A project requires an outlay of $1,000 at time 0 and pays $600 at the end of year 1 and $600 at the end of year 2. At an effective annual interest rate of 5%, what is the net present value?
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Correct answer: AThe net present value is -1,000+600/1.05+600/(1.05)^2. The two discounted receipts total approximately $1,088.44, giving an NPV of approximately $88.44.
A lender advances $5,000 at time 0 and receives $5,700 at time 2. Using annual effective compound interest, what is the annualized yield?
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Correct answer: BThe two-year accumulation factor is 5,700/5,000 = 1.14. Thus (1+i)^2 = 1.14, so i = √1.14 − 1 ≈ 0.0677, or 6.77%.
A bond has a redemption value of $1,000 and pays annual coupons of $60. It matures in 4 years. If the annual effective yield is 5%, which expression gives its price?
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Correct answer: AThe bond price is the present value of four end-of-year coupon payments plus the redemption value at year 4. Discount all cash flows at the required 5% yield, giving 60a-angle-4 at 5% + 1,000v^4 at 5%.
A fund accumulates according to the force of interest δ(t) = 0.02 + 0.01t, where t is measured in years. What is the accumulation factor from time 0 to time 2?
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Correct answer: BThe accumulation factor is exp(∫₀² δ(t)dt) = exp(∫₀²(0.02 + 0.01t)dt) = exp(0.04 + 0.02) = e^0.06. Thus option A is correct.
A perpetuity pays $240 at the end of each year. If the effective annual interest rate is 6%, what is its present value?
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Correct answer: AThe present value of a level perpetuity-immediate is payment divided by the effective rate: 240/0.06 = $4,000.
A bond has a par value of $1,000, a 6% annual coupon paid once per year, and a redemption value of $1,000 in 5 years. If its annual effective yield is 5%, is it priced at a premium, at par, or at a discount?
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Correct answer: AWhen a bond's coupon rate exceeds its yield, its coupons are relatively generous compared with market-required returns, so its price is above par. Here 6% > 5%, hence a premium.
A bond pays $40 at the end of each year for 4 years and returns $1,000 with the final coupon. Its purchase price is $950. Which equation determines its annual effective yield y?
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Correct answer: AEach coupon is discounted from its payment date, and the $1,000 redemption payment is discounted from year 4. Therefore the price equation is 950 = 40[(1-(1+y)^-4)/y] + 1000(1+y)^-4.
How to use this practice test
The free US Practice Tests practice bank contains 50 published questions, with each session drawing up to 20 random questions. Work each problem by laying out the cash-flow timeline and identifying the rate convention before calculating. Results appear after the session, so use missed items to pinpoint errors in discounting, payment timing, or yield equations.
Preparation tips
- For each cash-flow problem, draw a timeline and label whether each payment occurs at the beginning or end of a period before applying an annuity or discounting formula.
- Convert quoted rates carefully: distinguish effective interest from effective discount, and match the rate period to the cash-flow period.
- For bond valuation, separate coupon payments from redemption value, discount each at the yield, and check whether coupon rate and yield imply a premium, par, or discount price.
- When solving for yield, write the present-value equation first; then use a numerical method or calculator function if an algebraic solution is not practical.
- For a time-varying force of interest, integrate the force over the interval to obtain the accumulation factor, then apply it to the relevant cash flow.