This Exam FM sample reference tests College Fund Shortfall. The fund after the first payment and one year of growth is 12,569.46. The next required payment exceeds it by 1,870.26, so the shortfall is 1,870. The result agrees with the published answer key, choice E.
Accumulate the eighteen deposits of 750 to the first college-payment date. Then deduct the first tuition payment, whose amount has grown at 5% for seventeen years.
F17=750s18∣0.07=25499.27
Model
Model
Carry the remaining fund one year at 7% and compare it with the next tuition amount, which has grown for eighteen years.
F+=[25499.27−6000(1.05)17](1.07)=12569.46
Compute
Compute
The fund after the first payment and one year of growth is 12,569.46. The next required payment exceeds it by 1,870.26, so the shortfall is 1,870.
X=6000(1.05)18−12569.46=1870.26
Answer
Answer
The calculation gives 1870 for college fund shortfall, matching published choice E.
X=1870(E)
Continue without hunting through PDFs
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 (1439) does not match the checked college fund shortfall result (1870); no distinct standard one-step error is identifiable.
BChoice B (1545) does not match the checked college fund shortfall result (1870); no distinct standard one-step error is identifiable.
CChoice C (1664) does not match the checked college fund shortfall result (1870); no distinct standard one-step error is identifiable.
DChoice D (1785) does not match the checked college fund shortfall result (1870); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: present shortfall for an inflating tuition schedule
At the first tuition date, a college fund contains 50,000. Tuition of 14,000 is due immediately and at the next three anniversaries, increasing 3% each year. The fund earns 5% annually. Calculate the additional amount required at the first tuition date to exactly fund all four payments.
A 1,842.16
B 2,716.84
C 3,500.00
D 4,420.22
E 5,129.77
Variant answer in brief
The tuition stream is worth 54420.22 at the funding date, exceeding the available 50,000 by 4420.22. The required additional deposit is 4,420.22, which is choice D.
Setup
Setup
Use the first tuition date as time 0, so the first payment is not discounted.
Ck=14000(1.03)k,k=0,1,2,3
Model
Model
Discount the next three escalating payments at 5% and add them to the immediate 14,000.
PV=k=0∑3Ck(1.05)−k
Compute
Compute
The tuition stream is worth 54420.22 at the funding date, exceeding the available 50,000 by 4420.22.
PV=54420.220711,shortfall=PV−50000=4420.220711
Answer
Answer
The required additional deposit is 4,420.22, which is 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.
