This Exam FM sample reference tests Geometrically Increasing Deposits. Accumulating each of the ten geometrically increasing deposits at 4% gives a factor of 17.902263, so the first deposit is 279.29, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A discounts the growing deposits to time 0 but does not carry that value forward to time 10.
BChoice B treats the deposits as level and ignores their 9.2% annual growth.
CChoice C applies ten growth increases to the final deposit. There are only nine increases from deposit 1 to deposit 10.
EChoice E adds the 4% fund rate and 9.2% deposit growth as one rate instead of respecting the payment dates.
Original practice · fully worked
Original variant: accumulation of a growing reserve schedule
A laboratory deposits 250 at the end of year one into a reserve. Each later annual deposit is 5% larger than the preceding deposit, for a total of 12 deposits. The reserve earns 6% annually. Determine the value immediately after the twelfth deposit.
A 4,728
B 5,126
C 5,409
D 5,782
E 6,104
Variant answer in brief
Accumulating all 12 growing deposits at their individual dates gives 5,408.50, which is choice C.
Setup
Setup
Deposit t is 250 times 1.05 to the power t minus 1 and earns 6% until time 12.
Ct=250(1.05)t−1
Model
Model
Sum the time-12 value of all twelve deposits.
F12=250t=1∑12(1.05)t−1(1.06)12−t
Compute
Compute
Evaluating the finite sum gives 5,408.5036.
F12=5408.5036
Answer
Answer
The reserve holds approximately 5,409, so choice C is correct.
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.
