This Exam FM sample reference tests Simple and Compound Interest. The simple-interest account earns 70 in year 8, while the quarterly compound account earns 72.14; the absolute difference is 2.14, choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A compares rounded annual effective rates rather than the actual interest credited during year 8.
CChoice C uses the difference between the nominal annual rates on the original principal. It ignores quarterly compounding and the 7% rate applied by the simple account.
DChoice D is close to the difference between total account balances, not the interest credited during the eighth year alone.
EChoice E compares an accumulated balance with a one-year interest amount. Both quantities must cover the same year.
Original practice · fully worked
Original variant: six-year balance gap between crediting methods
A reserve places 2,000 in each of two accounts. Account S earns 6% annual simple interest. Account M earns a 4.8% nominal annual rate convertible monthly. No withdrawals occur. Determine the absolute difference between the two balances after six years.
A 4.70
B 28.36
C 54.02
D 120.00
E 185.98
Variant answer in brief
The simple-interest balance is 2,720.00 and the monthly compound balance is 2,665.98, giving an absolute difference of 54.02, choice C.
Setup
Setup
Compute each six-year balance under its own crediting rule.
AS=2000(1+0.06(6))
Model
Model
The monthly rate is 0.4%, and six years contain 72 monthly periods.
AM=2000(1+0.048/12)72
Compute
Compute
The two balances are 2,720.00 and 2,665.9826.
AS=2720.00
AM=2665.9826
∣AS−AM∣=54.0174
Answer
Answer
The absolute balance gap is approximately 54.02, 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.
