Worked solution · Exam FM
This Exam FM sample reference tests Spot and Forward Rates. Use time 0 as the comparison date. The opening balance and fifteen mid-month charges are borrowing inflows; fifteen month-end payments plus the 3,000 balance treated as an additional payment at month 15 are outflows. The expression with those exponents and fifteen terms is choice E.
Independent solution
Setup
Convert annual accumulation to fractional-year discounting and record each mid-month charge at time n minus one-half months.
Model
Record each payment at month-end and treat the final balance as an additional payoff at month 15.
Compute
Set opening balance plus charges equal to all payments and the terminal payoff.
Answer
This timing and exponent structure is the equation in choice E.
Test the method on unseen problems
30 original general cash flows, portfolios, and asset liability management problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Original practice · fully worked
A credit account earns 12% annual effective interest. During each of six months, 50 is charged at mid-month and 200 is paid at month-end. Immediately after the sixth payment, the balance is 500. Calculate the balance immediately before the first mid-month charge.
Discounting six payments and the ending balance, then subtracting the six mid-month charge values, gives opening balance 1,341.93, choice D.
Setup
Use the monthly accumulation factor equivalent to 12% annual effective.
Model
At time 0, opening balance plus charge present values equals payment present values plus the terminal balance present value.
Compute
Solving the present-value equation gives X = 1341.93.
Answer
The opening balance is 1,341.93, selecting choice D.
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