Worked solution · Exam FM
This Exam FM sample reference tests Mixed Interest-Rate Regimes. The three accumulation blocks are 12 quarters at 1%, three years at force 5%, and eight half-years at discount rate 3%. Their product grows 1000 to 1670.42, so choice C is correct.
Independent solution
Setup
Convert each quoted regime to the accumulation form that matches its conversion period.
Model
Apply the regimes consecutively for three, three, and four years.
Compute
The three factors compound to 1.67042424.
Answer
The account contains approximately 1670, which is choice C.
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Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
An account must contain 5,000 after seven years. It earns a nominal 6% rate convertible monthly for two years, a constant force of 4% for two years, and a nominal discount rate of 4% convertible quarterly for the final three years. Determine the required initial deposit.
The seven-year accumulation factor is 1.37754789. Dividing the 5000 target by this factor gives an initial deposit of 3629.64, choice D.
Setup
Translate the three regimes into monthly, continuous, and quarterly factors.
Model
Accumulate one initial dollar through all seven years.
Compute
The factor is 1.37754789, so solve for the initial principal P.
Answer
The required deposit is 3629.64, choice D.
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