Worked solution · Exam FM
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 solution
Setup
Discount the first zero's 2000 maturity value from year 5 to its year-3 purchase date.
Model
The stated year-3 outlay consists of that purchase plus one annual interest payment.
Compute
Isolate the interest amount and divide by principal.
Answer
The loan rate is 3.75%, choice D.
Test the method on unseen problems
30 original loans problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
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.
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.
Model
Deduct that asset cost from the total year-2 outlay.
Compute
Interest-only payment divided by loan principal is the annual rate.
Answer
The rate is 5.85%, choice D.
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