Final answer:
The incorrect expression for computing the equivalent present worth at period zero is option (a) P = $500(P/A, i, 4)(P/F, i, 4) as it illogically combines a present worth of an annuity and a present worth of a single future payment for the same period.
Step-by-step explanation:
Option (a) P = $500(P/A, i, 4)(P/F, i, 4) is incorrect, as it uses both a present worth of an annuity (P/A) and a present worth of a single future payment (P/F) for the same period, which does not make financial sense. The correct expression would separate the annuity and the single payment into two parts, without multiplying them together.
Options (b) P = $500(F/A, i, 4)(P/F, i, 7), (c) P = $500(P/A, i, 7) – $100(P/A, i, 3), and (d) P = $500[(P/F, i, 4) + (P/F, i, 5) + (P/F, i, 6) + (P/F, i, 7)] are more logically structured, as they apply formulas that would be used for annuities and single future payments in a manner that reflects their intended use. Option (b) computes the future worth of an annuity and then discounts it back to the present at a point different from when the annuity ends, option (c) combines two present worth of annuities, and option (d) sums the present values of multiple future payments.