This Exam FM sample reference tests Spot and Forward Rates. The ten 5,000 principals remain in the fund. Their annual 8% interest receipts form an increasing sequence of 400, 800, through 4,000, each reinvested at 5%. Principal plus accumulated interest equals 75654.30, or 75,700 to the nearest hundred; choice C.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (67,600) does not satisfy the sum of retained principal and the increasing annual interest receipts reinvested at 5%; no distinct standard one-step error is identifiable.
BChoice B (70,300) does not satisfy the sum of retained principal and the increasing annual interest receipts reinvested at 5%; no distinct standard one-step error is identifiable.
DChoice D (78,200) does not satisfy the sum of retained principal and the increasing annual interest receipts reinvested at 5%; no distinct standard one-step error is identifiable.
EChoice E (80,700) does not satisfy the sum of retained principal and the increasing annual interest receipts reinvested at 5%; no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: annual deposit required under separated interest reinvestment
At each of six year-beginnings, a reserve receives the same deposit D. Each deposited principal earns 7% annually, paid out at each year-end into a side account earning 2%; principal itself remains intact. Immediately after year 6 interest is credited, the combined accounts must total 70,000. Calculate D.
A 7,912.24
B 8,377.67
C 8,843.09
D 9,308.52
E 9,773.95
Variant answer in brief
Six retained deposits contribute 6D. Their annual 7% interest receipts form an increasing stream reinvested at 2%. The combined factor is 7.519992, giving D = 9,308.52, choice D.
Setup
Setup
The principal account contains six unchanged deposits at the terminal date.
P6=6D
Model
Model
Year k interest equals 0.07kD and is carried from year k to year 6 at 2%.
I6=0.07Dk=1∑6k(1.02)6−k
Compute
Compute
The combined coefficient is 7.51999184, so the required deposit is 9308.52.
70000=D(7.5199918386)
D=9308.52074074
Answer
Answer
Each annual deposit is 9,308.52, selecting choice D.
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.
