Worked solution · Exam FM
This Exam FM sample reference tests Immunization and Asset-Liability Management. The annuity price implies each liability payment is 4999.97. Exact immunization with one- and two-year zeros places the discounted second payment in the two-year bond, requiring 4535.12 today; choice B.
Independent solution
Setup
Recover the common annuity payment from its two-year present value at 5%.
Model
The two-year zero-coupon position must exactly fund the second payment.
Compute
The level payment is 4999.97, and its two-year present value is 4535.1220.
Answer
The company invests approximately 4,535 in the two-year zero, selecting choice B.
Test the method on unseen problems
30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
A three-year level annuity is exactly cash-flow matched with one-, two-, and three-year zero-coupon bonds at 4%. The insurer invests 4,000 today in the three-year zero. Calculate the present value of the full annuity.
The three-year zero grows to the common annuity payment 4,499.46. Multiplying that payment by the three-year annuity factor gives total annuity price 12,486.40, choice A.
Setup
Accumulate the three-year zero investment to its maturity; exact matching makes that maturity value the level payment.
Model
Value all three level payments at the same 4% yield.
Compute
The payment is 4499.46 and the full annuity price is 12486.40.
Answer
The annuity present value is 12,486.40, selecting choice A.
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