Under i = 0.05, the conversion of an m-period annuity due to an annual annuity due under the equivalence principle is given by which expression for a non-term annuity?

• A. Beta(m)
• B. alpha(m)*annual annuity due - Beta(m)
• C. alpha(m)
• D. annual annuity due - Beta(m)

Answer: (B)

Using the equivalence principle, you compare cash flows by their value at time 0. A non-term (perpetual) annuity-due pays 1 at the beginning of each year forever, with present value equal to the annual annuity-due amount. To represent the finite m-period annuity-due, you take only the portion of that perpetual stream up to year m and then subtract the value of everything that would occur after year m (the tail).

The factor α(m) scales the perpetual stream to reflect only the first m payments, and β(m) removes the tail beyond the m-th payment. Put together, the present value of the m-period annuity-due is expressed as α(m) times the annual annuity-due minus β(m). This structure exactly captures keeping the first m payments and discarding the rest, which is why that form is the correct conversion under the equivalence principle (at i = 0.05, the same principle applies with the same relationship between the factors). The other forms either fail to scale properly or fail to subtract the tail, so they wouldn’t match the finite cash-flow pattern.