This Exam FM sample reference tests Interest Rate Valuation. Equating the compound account force ln(1.07) to the simple-interest force after two years gives y = 7.825%; the simple-interest account then equals 1,156.5, nearest choice A.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
BChoice B is inconsistent with the time-dependent force of simple interest; no distinct standard single-step error producing it is identifiable.
CChoice C is inconsistent with the time-dependent force of simple interest; no distinct standard single-step error producing it is identifiable.
DChoice D is inconsistent with the time-dependent force of simple interest; no distinct standard single-step error producing it is identifiable.
EChoice E is inconsistent with the time-dependent force of simple interest; no distinct standard single-step error producing it is identifiable.
Original practice · fully worked
Original variant: matching maintenance-account forces
A building reserve compounds at 6% effective annually. A separate account receives 2,000 at time 1 and earns simple interest at annual rate y. At time 5 the two accounts have equal instantaneous forces. Find the second account's value at time 5.
A 2,400.00
B 2,500.00
C 2,607.82
D 2,720.00
E 2,800.00
Variant answer in brief
Force equality gives y = 7.5977%, and four years of simple accumulation gives 2,607.82, choice C.
Setup
Setup
The simple-interest account has run for four years when the instantaneous rates are compared.
δ=ln(1.06),1+4yy=δ
Model
Model
Equating its current force to the constant force of the compound account isolates y.
y=1−4δδ=0.0759774
Compute
Compute
The resulting simple rate is 0.0759774; inserting it in the four-year accumulation function gives 2,607.819.
A=2000(1+4y)=2607.819
Answer
Answer
The account value is therefore 2,607.82, 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.
