Worked solution · Exam FM
This Exam FM sample reference tests Principal and Interest in a Growing Payment. The first installment is 2091.51 and the second is 2300.66. Just before the second payment the balance is 19708.49; its 9% interest is 1773.76, leaving 526.89 of principal, choice B.
Independent solution
Setup
Let R be the first payment. Price the ten payments growing at 10% using the 9% loan rate.
Model
The first payment is 2091.51 and the second is 2300.66.
Compute
Value payments 2 through 10 just before payment 2 to obtain the interest base.
Answer
The second installment repays about 527 of principal, choice B.
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 six-payment annual loan schedule begins with 2,500 at the end of year 1, and each later payment is 5% smaller than the preceding payment. The loan rate is 6% effective annually. Determine the interest portion of the fifth payment.
Immediately after payment 4, the present value of payments 5 and 6 is 3642.66. Six percent interest on that balance is 218.56, choice B.
Setup
Payments 5 and 6 are the only cash flows remaining after payment 4.
Model
Value both payments at time 4.
Compute
The next year's interest is 6% of this post-payment balance.
Answer
The fifth payment contains 218.56 of interest, choice B.
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