This Exam FM sample reference tests Deferred Increasing Annuity. The direct discounted sum is 64,257, which is the loan value. The result agrees with the published answer key, choice D.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (58,283) does not match the checked deferred increasing annuity result (64,257); no distinct standard one-step error is identifiable.
BChoice B (61,197) does not match the checked deferred increasing annuity result (64,257); no distinct standard one-step error is identifiable.
CChoice C (64,021) does not match the checked deferred increasing annuity result (64,257); no distinct standard one-step error is identifiable.
EChoice E (69,211) does not match the checked deferred increasing annuity result (64,257); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: deferred ten-payment increasing maintenance annuity
A facility contract pays 500 at time 4, then increases each annual payment by 100 through the tenth payment at time 13. At a 5% annual effective rate, calculate the time-0 value.
A 5,544.82
B 5,788.51
C 6,069.39
D 6,306.40
E 6,554.13
Variant answer in brief
The ten discounted payments total 6069.39. The contract value is 6,069.39, corresponding to choice C.
Setup
Setup
Index each of the ten payments and map payment k to time k + 3.
Pk=500+100(k−1),tk=k+3,k=1,…,10
Model
Model
Discount the increasing cash-flow vector directly to time 0, retaining the three-year deferment before the first payment.
PV=k=1∑10Pk(1.05)−(k+3)
Compute
Compute
The ten discounted payments total 6069.39.
PV=6069.385381
Answer
Answer
The contract value is 6,069.39, corresponding to choice C.
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