This Exam FM sample reference tests Equivalent Yield on Irregular Deposits. Solving gives r₂ = 9.3637% per two years. The equivalent annual rate is the square root of 1 + r₂ minus 1, equal to 4.577%, or 4.58%. The result agrees with the published answer key, choice D.
How to solve this Equivalent Yield on Irregular Deposits question
Setup
Setup
Accumulate each beginning-of-year deposit through the sequence of credited rates to the common terminal date. Group deposits made under the same rate regime with annuity-due factors.
A=100s¨3∣0.0816(1.05)4+100s¨2∣0.1025=659.269
Model
Model
The actual accumulated value is 659.269. Set this equal to five beginning-of-period deposits under a constant two-year effective rate r₂.
100s¨5∣r2=659.269⟹r2=0.093637
Compute
Compute
Solving gives r₂ = 9.3637% per two years. The equivalent annual rate is the square root of 1 + r₂ minus 1, equal to 4.577%, or 4.58%.
i=(1+r2)1/2−1=0.04577
Answer
Answer
The calculation gives 4.58% for equivalent yield on irregular deposits, matching published choice D.
i=4.58%(D)
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All 461 Exam FM sample solutions in syllabus order
The searchable 2210-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (4.18%) does not match the checked equivalent yield on irregular deposits result (4.58%); no distinct standard one-step error is identifiable.
BChoice B (4.40%) does not match the checked equivalent yield on irregular deposits result (4.58%); no distinct standard one-step error is identifiable.
CChoice C (4.50%) does not match the checked equivalent yield on irregular deposits result (4.58%); no distinct standard one-step error is identifiable.
EChoice E (4.78%) does not match the checked equivalent yield on irregular deposits result (4.58%); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: yield on two irregular deposits and one terminal fund
A research account receives 1,000 at time 0 and 1,500 at time 2. The account value is 3,000 at time 5, with no other cash flows. Calculate the annual effective yield.
A 2.88%
B 3.88%
C 4.88%
D 5.88%
E 6.88%
Variant answer in brief
A bracketed root solve gives annual effective yield 4.8846%. Rounded to two decimals, the yield is 4.88%, which is choice C.
Setup
Setup
Move both deposits to time 5; the first earns five years and the second earns three.
1000(1+i)5+1500(1+i)3=3000
Model
Model
The resulting polynomial is increasing for positive i, so its positive root is the unique yield.
f(i)=1000(1+i)5+1500(1+i)3−3000
Compute
Compute
A bracketed root solve gives annual effective yield 4.8846%.
f(i)=0⟹i=0.04884582
Answer
Answer
Rounded to two decimals, the yield is 4.88%, which is choice C.
i=4.88%(C)
Calculator reproduction
BA II Plus keystrokes
CF; 2nd CLR WORK; 1000 +/- CF0; 0 C01; 1 F01; 1500 +/- C02; 0 C03; 2 F03; 3000 C04; IRR; CPT4.8846Equivalent IRR worksheet entry with years represented as periods.
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.
