Worked solution · Exam FM
This Exam FM sample reference tests Interest Rate Measures. The first loan's observed monthly interest is P1 − P0 + m, so its nominal annual rate is 12 times that amount divided by P0. Loan B credits one 365th of the nominal rate daily for 365/12 days per month; this is the expression in choice E.
Independent solution
Setup
Use the first loan's one-month balance equation to isolate the month's interest.
Model
Convert the resulting monthly effective rate to the shared nominal annual rate, then to Loan B's daily periodic rate.
Compute
Accumulate the daily rate through 365/12 days in one equal month.
Answer
The resulting expression is listed in choice E.
Test the method on unseen problems
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.
Original practice · fully worked
A loan starts a month at 10,000, receives a month-end payment of 900, and then has balance 9,150. Its nominal annual rate is shared by another loan that compounds daily using 365 days and twelve equal months. Calculate the second loan's effective monthly rate.
The observed interest is 50, implying 0.5% monthly and a 6% nominal annual rate. Compounding one 365th of 6% for 365/12 days gives effective monthly rate 0.5012%, choice D.
Setup
Recover the first loan's monthly interest from its balance change.
Model
Annualize nominally and apply the daily rate for one equal month.
Compute
The daily-compounded monthly rate is 0.501211%.
Answer
The second loan's effective monthly rate is 0.5012%, selecting choice D.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 51 Exam FM time value of money practice problems.
Drill the method: Exam FM Annual Force of Interest and Rate Conversion problems
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