Verified solution · Exam FM

SOA Exam FM Sample Question #343 Solution

This Exam FM sample reference tests Interest-Only Loan with Dedicated Zero-Coupon Assets. At year 3, the first zero costs 1885.19. The rest of the 2260.19 outlay is the loan's annual interest of 375, so the rate is 3.75% and choice D.

Independent analysis by ActuaryProof · reviewed August 4, 2026

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

Read the solution Open official source

Independent solution

How to solve this Interest-Only Loan with Dedicated Zero-Coupon Assets question

Setup

Discount the first zero's 2000 maturity value from year 5 to its year-3 purchase date.

P_{Z1}=\frac{2{,}000}{1.03^2}=1{,}885.1918

Model

The stated year-3 outlay consists of that purchase plus one annual interest payment.

10{,}000i+1{,}885.1918=2{,}260.19

Compute

Isolate the interest amount and divide by principal.

10{,}000i=374.9982

i=0.0374998

Answer

The loan rate is 3.75%, choice D.

\boxed{i\approx3.75\%\quad\text{(D)}}

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.

See inside the Exam FM study manual PDF

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 discounts the 2000 zero for three years instead of the two years remaining after its purchase.
BChoice B copies the zero's yield and ignores the separate interest payment in the outlay.
CChoice C uses the second zero's 2.5% yield to price the first zero.
EChoice E subtracts the zero's par amount rather than its year-3 purchase price from the total outlay.

Original practice · fully worked

Original variant: loan rate from a sinking-asset purchase

A 20,000 interest-only loan has annual interest payments and principal due at year 5. At year 2, the borrower spends 3,000 in total on that year's interest and a zero-coupon asset paying 2,000 at year 5. The asset yields 3% annually. Determine the loan's annual effective rate.

A
3.92%
B
4.67%
C
5.25%
D
5.85%
E
6.30%

Variant answer in brief

The zero costs 1830.28 at year 2, leaving 1169.72 for annual loan interest. Relative to principal 20000, the rate is 5.8486%, choice D.

Setup

Value the year-5 zero at its year-2 purchase date.

P_Z=\frac{2{,}000}{1.03^3}=1{,}830.2833

Model

Deduct that asset cost from the total year-2 outlay.

I=3{,}000-1{,}830.2833=1{,}169.7167

Compute

Interest-only payment divided by loan principal is the annual rate.

i=\frac{1{,}169.7167}{20{,}000}=0.0584858

Answer

The rate is 5.85%, choice D.

\boxed{i\approx5.85\%\quad\text{(D)}}

Keep practicing

Turn this solution into a complete study sequence

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.

See the Exam FM study manual PDF — $49 More Exam FM Loans practice problems Free Exam FM formula sheet

Cite this solution

ActuaryProof. “SOA Exam FM Sample Question #343 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Interest-Only Loan with Dedicated Zero-Coupon Assets question

Setup

Model

Compute

Answer

All 461 Exam FM sample solutions in syllabus order

Why the other letters tempt

Original variant: loan rate from a sinking-asset purchase

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam FM solutions

Turn this solution into a complete study sequence

Cite this solution