Worked solution · Exam FM
This Exam FM sample reference tests Interest Credited over a Specified Year. Under force 1/(t+1), the first account grows from 9 at time 2 to 12 at time 3, earning 3 during the third year. The corresponding bank-account interest factor is 0.055125, giving X = 54.42 and choice E.
Independent solution
Setup
Integrating the force gives an accumulation proportional to t plus 1. The initial deposit of 3 therefore has value 3(t+1).
Model
Interest earned during the third year is the value increase from time 2 to time 3.
Compute
The bank account's third-year interest is the difference of its time-3 and time-2 values.
Answer
The required bank deposit is 54.4, 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.
Error diagnosis
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Original practice · fully worked
A deposit of 5 is placed in a fund with force of interest 2 divided by t plus 2. Another deposit X earns 4% effective annually. Find X so that the interest earned during the second year, from time 1 to time 2, is the same in both accounts.
The force-based account earns 8.75 during year 2. Dividing by 1.04 squared minus 1.04 gives X = 210.34, choice D.
Setup
Integrating 2/(t+2) makes the first balance proportional to (t+2) squared.
Model
Compute its increase from time 1 to time 2.
Compute
Set this equal to second-year interest in the 4% account.
Answer
The matching deposit is 210.34, choice D.
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