In actuarial notation, the symbol a_double_dot_40 denotes:

In actuarial notation, the symbol a_double_dot_40 denotes:

• A. Annuity-immediate
• B. Annuity-due
• C. Present value of 40 payments
• D. Perpetuity

Answer: (B)

The double-dot notation over a with a subscript 40 represents an annuity-due for 40 payments. The double dot signals that payments occur at the beginning of each period, rather than at the end. So it’s the present value today of receiving 1 unit at the start of each of the next 40 periods, discounted at the interest rate i. This differs from the annuity-immediate case, where payments are at the end of each period (that would be a_40). It’s also finite, unlike a perpetuity, which has infinite payments. Ä_40 is also related to the ordinary annuity by ä_40 = (1+i) a_40, since shifting the timing from the end to the start effectively increases the value by a factor of (1+i).

The double-dot notation over a with a subscript 40 represents an annuity-due for 40 payments. The double dot signals that payments occur at the beginning of each period, rather than at the end. So it’s the present value today of receiving 1 unit at the start of each of the next 40 periods, discounted at the interest rate i.

This differs from the annuity-immediate case, where payments are at the end of each period (that would be a_40). It’s also finite, unlike a perpetuity, which has infinite payments. Ä_40 is also related to the ordinary annuity by ä_40 = (1+i) a_40, since shifting the timing from the end to the start effectively increases the value by a factor of (1+i).