If the future value of an annuity is known, then the present value of the annuity can be found using the present value of a lump sum formula, even if the amount of each annuity payment is unknown.

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BlackTom AI · Accepted Answer

The statement asks whether knowing the future value of an annuity allows us to find its present value using the lump-sum PV formula, even if the individual payment amounts are unknown.
First, consider what the future value of an annuity represents: it's the accumulated value of a series of payments over time, taking into account the interest earned on each payment. The present value, on the other hand, is the sum of the discounted payments back to the present using the time value of money.
Option 1: True. This would imply that the present value can be obtained by simply discounting a single future lump sum that equals the annuity’s future value. However, this is not generally valid because the FV of an annuity aggregates multiple payments, each of which has its own timing and discounting. A single lump-sum discount factor cannot capture the distribution of multiple payments unless you know the exact payment pattern. Therefore using a simple FV-to-PV lump-sum formula is inappropriate when payment amounts are unknown.
Option 2: False. This option aligns with the fundamental idea that an annuity’s FV depends on the sequence of multiple payments, not a single amount. To recover present value from a known FV, you would need to know the payment schedule (amounts and timing) and then discount each payment back to present value, or use the standard PV of annuity formulas once payments are specified. Without the payment amounts, you cannot correctly apply a lump-sum PV formula to obtain the present value, because the lump-sum approach ignores the distribution of payments over time.
In summary, the misstep in the statement is treating the annuity’s future value as if it were a single future amount that can be discounted with the lump-sum formula, ignoring the necessity of knowing payment amounts and their timing. The correct view is that you cannot reliably find the present value from the known future value of an annuity without additional information about the payment structure.

MCD2170 - T1 - 2025 Key Concept 2 Video quiz

If the future value of an annuity is known, then the present value of the annuity can be found using the present value of a lump sum formula, even if the amount of each annuity payment is unknown.

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