This Exam FM sample reference tests Reinvestment of Interest. Separating the 50,000 of deposited principal from reinvested interest gives i = 15.592%, so the answer is choice B.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A understates the interest contribution by treating the deposits as end-of-year rather than beginning-of-year cash flows.
CChoice C fails to subtract the 50,000 of deposited principal before solving for the earned-interest rate.
DChoice D reinvests the principal as well as the interest at 5%, contrary to the stated separation.
EChoice E omits the division by the 5% reinvestment rate in the accumulated-interest series.
Original practice · fully worked
Original variant: terminal fund with separately reinvested earnings
A cooperative deposits 3,000 at the beginning of each year for eight years. Each deposit earns annual interest equal to 12% of its original principal, and every interest credit is reinvested at 4% annually. Determine the fund at the end of year eight.
A 33,518
B 36,804
C 38,245
D 40,000
E 42,617
Variant answer in brief
The 24,000 of principal plus accumulated reinvested interest produces 38,245.16 at time 8, which is choice C.
Setup
Setup
The deposits contribute 24,000 of principal. Treat the annual interest credits as a separate cash-flow stream.
P=8(3000)=24000
Model
Model
Each active deposit earns 360 per year. Accumulating the triangular pattern of interest credits at 4% gives the standard annuity-due difference factor.
I8=3000(0.12)0.04s¨8∣0.04−8
Compute
Compute
The annuity-due accumulated factor is 9.582795, so reinvested interest contributes 14,245.16.
I8=3600.049.582795−8=14245.16
F8=24000+14245.16=38245.16
Answer
Answer
The ending fund is approximately 38,245, so the correct choice is C.
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