This Exam FM sample reference tests Spot and Forward Rates. Expressing the contractual payment as L divided by the ten-year annuity factor and accumulating the first four receipts at 10% and the final six at 7% gives a terminal-value ratio of 2.297669. Its tenth root yields 8.67%, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (7.90%) does not satisfy the split terminal-value equation for four 10% and six 7% reinvestment years; no distinct standard one-step error is identifiable.
BChoice B (8.20%) does not satisfy the split terminal-value equation for four 10% and six 7% reinvestment years; no distinct standard one-step error is identifiable.
CChoice C (8.33%) does not satisfy the split terminal-value equation for four 10% and six 7% reinvestment years; no distinct standard one-step error is identifiable.
EChoice E (9.10%) does not satisfy the split terminal-value equation for four 10% and six 7% reinvestment years; no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: later reinvestment rate implied by a target realized loan yield
A unit loan is amortized by eight annual payments calculated at 8%. The first three receipts are reinvested at 8%; all balances and later receipts then earn a constant rate x for the final five years. Find x if the lender's realized eight-year annual yield is 7%.
A 5.38%
B 5.66%
C 5.94%
D 6.22%
E 6.51%
Variant answer in brief
The contractual payment is 0.174015 per unit lent. Equating the split reinvestment fund to 1.07 raised to the eighth power gives x = 5.66%, choice B.
Setup
Setup
Compute the annual payment on the unit loan from the contractual 8% amortization basis.
R=a8∣0.081
Model
Model
Accumulate the first three payments to year 3 at 8%, then carry that balance and the final five payments at the unknown rate.
F8=R[s3∣0.08(1+x)5+s5∣x]
Compute
Compute
Set the fund equal to the target eight-year accumulation and solve numerically, giving x = 5.6589%.
F8=(1.07)8
x=0.05658907
Answer
Answer
The required later reinvestment rate is 5.66%, which is choice B.
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.
