Worked solution · Exam FM
This Exam FM sample reference tests Annuities. Discounting the time-25 balance and all deposits through the two interest-rate regimes requires 3% factors through year 10 and 2% factors thereafter. The only expression with the correct split and timing is choice D.
Independent solution
Setup
Index the 26 beginning-of-year deposits at times 0 through 25 and use time 0 as the comparison date.
Model
Deposits before or at time 10 use only the 3% discount curve; later deposits first cross the 2% segment after time 10.
Compute
Equate the discounted target balance at time 25 to the two groups of discounted deposits.
Answer
This is exactly the equation displayed in choice D.
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Original practice · fully worked
A saver deposits the same amount at times 0, 1, 2, 3, 4, and 5. The account earns 4% in each of the first three years and 3% in each of the next two years. Immediately after the time-5 deposit the balance must be 50,000. Calculate each deposit.
Accumulating each of the six deposits through the appropriate 4% and 3% periods gives a combined factor of 6.535074. Dividing 50,000 by that factor gives deposit 7,651.02, choice C.
Setup
Use time 5 as the comparison date and retain the exact rate regime traversed by each deposit.
Model
Factor out the common deposit and set the accumulated value equal to the target balance.
Compute
The accumulation coefficient is 6.535074, so D = 7651.02.
Answer
Each deposit is 7,651.02, selecting choice C.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 113 Exam FM annuities and non-contingent cash flows practice problems.
Drill the method: Exam FM Annuities and Perpetuities problems
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