Which term describes an annuity that starts after a fixed time and continues forever?

Which term describes an annuity that starts after a fixed time and continues forever?

• A. A constant sum of money paid or received each period for a given number of periods.
• B. An annuity that starts after a fixed time and continues forever.
• C. A measure of how long until the initial investment is recovered.
• D. The return required by the company's investors.

Answer: (B)

An annuity that continues forever is a perpetuity. When it starts after a fixed delay, it’s a deferred perpetuity—the payments are constant, run indefinitely, but begin after that deferral period. In valuation terms, the value today of a perpetuity paying PMT each period is PMT divided by the discount rate (PMT/r) if it starts immediately. If the payments begin after n periods, you take that immediate value and discount it back n periods, giving (PMT/r) / (1+r)^n. For example, if PMT is 100 and the rate is 5%, a perpetuity starting now is worth 100/0.05 = 2000. If it starts after 3 years, its present value is 2000 / (1.05)^3 ≈ 1738. This matches the description of a cash flow that begins after a fixed time and continues forever. The other concepts describe finite cash flows, payback timing, or required returns, none of which capture the idea of an infinite, deferrable series.

An annuity that continues forever is a perpetuity. When it starts after a fixed delay, it’s a deferred perpetuity—the payments are constant, run indefinitely, but begin after that deferral period. In valuation terms, the value today of a perpetuity paying PMT each period is PMT divided by the discount rate (PMT/r) if it starts immediately. If the payments begin after n periods, you take that immediate value and discount it back n periods, giving (PMT/r) / (1+r)^n.

For example, if PMT is 100 and the rate is 5%, a perpetuity starting now is worth 100/0.05 = 2000. If it starts after 3 years, its present value is 2000 / (1.05)^3 ≈ 1738.

This matches the description of a cash flow that begins after a fixed time and continues forever. The other concepts describe finite cash flows, payback timing, or required returns, none of which capture the idea of an infinite, deferrable series.