Free SOA Exam FM (Financial Mathematics) Bonds Practice Questions
Bond pricing and yield calculations on SOA Exam FM test par, premium, and discount bonds, callable bonds, yield curves, and Macaulay and modified duration. Bond valuation is one of the most heavily weighted topics on the exam.
224 questions87 easy76 medium61 hard2026 syllabus
Sample Questions
Question 1
Easy
A bond is said to be "callable" if:
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Correct Answer: B
Solution
B is correct.
A callable bond gives the issuer (not the bondholder) the right to redeem the bond before its stated maturity date, typically at a specified call price.
Question 2
Medium
Which of the following correctly describes a premium bond's amortization schedule?
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Correct Answer: D
Solution
D is correct.
For a premium bond (P>C), we have Fr>Cj. The book value starts above C and decreases each period toward C. The amortization of premium in period t is PAt=Fr−j⋅Bt−1. Since Bt−1 decreases over time, j⋅Bt−1 decreases, making PAt larger. So the amortization of premium increases each period. Book value decreases and amortization amounts increase.
Question 3
Hard
A 1,000 par value 20-year bond with 6% annual coupons is purchased at par. Coupons are reinvested at 4%. Calculate the annual realized yield over the 20-year period.
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Correct Answer: E
Solution
E is correct.
The bond is bought at par, so P=1,000 and each annual coupon is 0.06⋅1,000=60.
Coupons accumulate at the reinvestment rate of 4%: s20∣0.04=0.04(1.04)20−1=0.042.191123−1=29.778079.
Accumulated value at maturity (reinvested coupons plus redemption of par): AV=60(29.778079)+1,000=1,786.68+1,000=2,786.68.
The realized annual yield j satisfies P(1+j)20=AV: j=(1,0002,786.68)1/20−1=(2.78668)0.05−1.
Using ln(2.78668)=1.02485, we get 201.02485=0.051243 and e0.051243=1.05258.
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