This Exam FM sample reference tests Geometrically Increasing Deposits. Writing the 120 beginning-of-month deposits as ten annual blocks gives a year-1 monthly deposit of essentially 100. The year-5 amount is 100 times 1.1 to the fourth, or 146.41, choice C.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A applies only three 10% increases to the inferred first-year deposit.
BChoice B values deposits at month end instead of month beginning and then compounds the resulting first-year amount.
DChoice D rounds the monthly rate conversion or the first-year amount before the fourth growth step.
EChoice E treats 2.4% nominal as 2.4% effective over each month in part of the accumulation.
Original practice · fully worked
Original variant: accumulate yearly increasing monthly deposits
A saver deposits 200 at the beginning of every month in year 1. At the start of each later year, the monthly deposit rises by 5%. The account earns a nominal annual rate of 3.6% compounded monthly. Determine the balance at the end of year 6 after all 72 deposits.
A 15,816.40
B 16,940.22
C 17,506.13
D 18,152.96
E 19,060.61
Variant answer in brief
Accumulate each of the six twelve-payment blocks to month 72 at 0.3% per month. The resulting balance is 18152.96, choice D.
Setup
Setup
The monthly rate is 0.3%, and deposits within year k have amount 200 times 1.05 to the k.
j=0.036/12=0.003
Model
Model
Index years from zero and months within a year from zero. A beginning-month deposit at month 12k plus m grows to month 72.
S=k=0∑5m=0∑11200(1.05)k(1.003)72−(12k+m)
Compute
Compute
Evaluate the six blocks without rounding their intermediate balances.
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.
