Which sequence shows the mid-year discount factors for five periods in a mid-year DCF?

Which sequence shows the mid-year discount factors for five periods in a mid-year DCF?

• A. 0.5, 1.0, 1.5, 2.0, 2.5
• B. 0.5, 1.5, 2.5, 3.5, 4.0
• C. 1.0, 2.0, 3.0, 4.0, 5.0
• D. 0.5, 1.5, 2.5, 3.5, 4.5

Answer: (D)

Mid-year convention uses half-year time points for discounting, reflecting cash flows that arrive halfway through each year. For five periods, the appropriate discount times are 0.5, 1.5, 2.5, 3.5, and 4.5 years, with discount factors 1/(1+r)^{t} at those t-values. This half-year offset ensures every cash flow is tied to the mid-point of its year. The other sequences don’t maintain that consistent 0.5-year shift (they mix or use whole-year timings), so they don’t represent mid-year discounting.

Mid-year convention uses half-year time points for discounting, reflecting cash flows that arrive halfway through each year. For five periods, the appropriate discount times are 0.5, 1.5, 2.5, 3.5, and 4.5 years, with discount factors 1/(1+r)^{t} at those t-values. This half-year offset ensures every cash flow is tied to the mid-point of its year. The other sequences don’t maintain that consistent 0.5-year shift (they mix or use whole-year timings), so they don’t represent mid-year discounting.