This Exam FM sample reference tests Geometrically Increasing Coupons. At j = 1.9804%, the coupon coefficient is 12.015 and redemption is worth 197.579. Solving gives c = 32.04. The result agrees with the published answer key, choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B (32.68) does not match the checked geometrically increasing coupons result (32.04); no distinct standard one-step error is identifiable.
CChoice C (40.22) does not match the checked geometrically increasing coupons result (32.04); no distinct standard one-step error is identifiable.
DChoice D (48.48) does not match the checked geometrically increasing coupons result (32.04); no distinct standard one-step error is identifiable.
EChoice E (49.45) does not match the checked geometrically increasing coupons result (32.04); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: six-year bond with geometrically increasing coupons
A six-year bond pays a coupon of 20 at the end of year 1, with each later coupon 5% larger than the preceding coupon. It redeems 500 at year 6. At a 4% annual effective yield, calculate the price.
A 482.18
B 500.44
C 513.35
D 526.92
E 540.00
Variant answer in brief
The coupon stream and redemption sum to price 513.35. The bond price is 513.35, selecting choice C.
Setup
Setup
Write each coupon from its 5% geometric growth rule and combine the sixth coupon with redemption only after preserving its amount.
Ct=20(1.05)t−1,t=1,…,6
Model
Model
Discount the six coupons and the 500 redemption at 4%.
P=t=1∑6Ct(1.04)−t+500(1.04)−6
Compute
Compute
The coupon stream and redemption sum to price 513.35.
The 2210-page Financial Mathematics Proof Manual reorganizes 461 verified Exam FM solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
