The value of a five-year annuity is equal to the sum of two perpetuities. One makes its first payment in year 1, and the other makes its first payment in year 6.

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The value of a five-year annuity cannot be equal to the sum of two perpetuities with the described payment schedules because an annuity has a finite number of payments, while perpetuities have infinite payments. The value of an annuity is calculated based on a limited number of payments, whereas perpetuities are valued based on an infinite series of payments.

The Value of a Five-Year Annuity Is Equal to the Sum