Worked solution · Exam FM

SOA Exam FM Sample Question #438 Solution

This Exam FM sample reference tests Implied Short-Term Credit Yield. At day 15, paying late replaces 0.975X with 250 plus X minus 250 due 45 days later. Discounting at the 45-day rate equivalent to 24.2% annually gives X = 4827.18, choice E.

Independent analysis by ActuaryProof · reviewed October 6, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

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Independent solution

How to solve this Implied Short-Term Credit Yield question

Setup

Use day 15 as the comparison date. Let q be the 45-day accumulation factor implied by the annual effective yield.

q=(1.242)^{45/365}

Model

The discounted full-payment option must equal the value of the installment option at day 15.

0.975X=250+\frac{X-250}{q}

Compute

Solve the linear equation after computing q = 1.02707943.

X=\frac{250(q-1)}{0.975q-1}

X=4{,}827.178

Answer

The full treatment price rounds to 4827, choice E.

\boxed{X\approx4{,}827\quad\text{(E)}}

Test the method on unseen problems

Financial Mathematics Practice Examination I

30 original Exam FM questions across the syllabus, to be worked in 150 timed minutes, with a full worked solution for each one. Written for Exam FM, not copied from the SOA set. One-time $39 PDF.

See the cover and sample pages

Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

AChoice A treats the 2.5% discount as 2.5% of the 250 initial installment rather than of the full price.
BChoice B annualizes the 45-day charge by simple interest before solving the payment equivalence.
CChoice C discounts the entire X minus 250 balance from day 60 but omits the day-15 payment.
DChoice D compares day-15 and day-60 dollars directly without converting the annual yield to 45 days.

Original practice · fully worked

Original variant: annualize a deferred balance charge

A clinic lists a procedure at 3,000. Option A requires 2,940 on day 10. Option B requires 500 on day 10 and 2,500 on day 70. Treating the two options as financially equivalent, determine the implied effective annual yield on the deferred balance, using a 365-day year.

A
10.17%
B
12.30%
C
15.93%
D
18.25%
E
24.59%

Answer and calculation

At day 10, the delayed 2500 replaces 2440 of immediate value for 60 days. Annualizing the ratio 2500 divided by 2440 gives 15.93%, choice C.

Setup

Subtract the common day-10 portion to identify the amount actually financed.

2{,}940-500=2{,}440

Model

Let i be the effective annual yield. Sixty days of accumulation carries 2440 to the day-70 payment of 2500.

2{,}440(1+i)^{60/365}=2{,}500

Compute

Annualize the observed 60-day accumulation ratio.

i=\left(\frac{2{,}500}{2{,}440}\right)^{365/60}-1

i=0.1592585

Answer

The implied annual yield is 15.93%, choice C.

\boxed{i\approx15.93\%\quad\text{(C)}}

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How to solve this Implied Short-Term Credit Yield question

Setup

Model

Compute

Answer

Financial Mathematics Practice Examination I

Why the other letters tempt

Original variant: annualize a deferred balance charge

Answer and calculation

Setup

Model

Compute

Answer

Related Exam FM solutions

Next steps for Exam FM Time Value of Money