This Exam FM sample reference tests Stepped and Level Perpetuities. Discount the five scheduled payments individually and value the level tail from its first payment date. Their sum is 5917.19, which selects D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AThe value 5249 is too small to include both the five due payments and the level tail beginning after the fifth payment.
BThe value 5530 does not equal the sum of the separately discounted stepped segment and the fifth-payment-level tail.
CThe value 5617 is consistent with shortening or misdating the tail; the tail actually starts at time five.
EThe value 6046 overstates the tail by allowing the payment to keep growing after the fifth amount has been reached.
Original practice · fully worked
Original variant: determine the level reserve payment
A maintenance reserve is worth 8,000 today. It pays 600 at the end of year 1, 660 at the end of year 2, and 726 at the end of year 3. Beginning at the end of year 4, it pays the same amount T forever. At an annual effective rate of 8%, determine T.
A 588.08
B 617.13
C 635.12
D 685.93
E 726.00
Variant answer in brief
The first three payments have present value 1697.72. Equating the remaining value to a perpetuity whose first payment is at time 4 gives T = 635.12.
Setup
Setup
Value every cash flow at time zero and reserve the symbol T for the new level tail.
v=(1.08)−1
Model
Model
The first level payment is four years away, so the tail value is T times v to the fourth divided by one minus v.
8,000=600v+660v2+726v3+T1−vv4
Compute
Compute
The known payments account for 1697.721 of present value. Solve the remaining linear term.
T=(8,000−1,697.721)v41−v
T=635.124
Answer
Answer
The required permanent payment is 635.12, which is choice C.
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.
