Worked solution · Exam FM
This Exam FM sample reference tests Geometrically Increasing Loan Payments. The initial payment is 2584.39 from the ten-payment growing-annuity loan equation. After payment 8 only payments 9 and 10 remain; their value at time 8 is 7353.15, choice C.
Independent solution
Setup
Let X be the first year-end payment. Payment k is X times 1.06 to the k minus one.
Model
Price all ten payments at the 10% loan rate.
Compute
The equation gives X = 2584.391. Value the final two payments immediately after payment 8.
Answer
The outstanding balance is approximately 7353, choice C.
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 borrower promises eight annual payments, beginning with 3,000 at the end of year 1. Each later payment is 3% smaller than the preceding one. At a 5% annual effective loan rate, determine the original principal advanced.
Discounting the eight payments 3000 times 0.97 to successive powers at 5% gives an original principal of 17607.44, choice D.
Setup
Payment k equals 3000 times 0.97 to the k minus one.
Model
The principal is the present value of all eight promised payments.
Compute
Evaluate the finite geometric series.
Answer
The loan principal is 17607.44, choice D.
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