Annuity due意思

Annuity Due, also known as an immediate annuity, is a type of annuity in which payments are made at the beginning of each period rather than at the end, as is the case with an ordinary annuity. In other words, with an annuity due, the first payment is made immediately upon entering into the annuity contract, and subsequent payments are made at the beginning of each subsequent period.

The main difference between an annuity due and an ordinary annuity is the timing of the payments. The cash flow pattern for an annuity due is as follows:

• First payment at the beginning of the first period (t=0).
• Subsequent payments at the beginning of each period (t=1, t=2, etc.).

Because of the different timing of payments, the present value (PV) of an annuity due is typically higher than the present value of an ordinary annuity with the same cash flows. The formula for the present value of an annuity due is:

PV = C / r + (C / r)^2 + (C / r)^3 + ... + (C / r)^n

Where:

• PV is the present value of the annuity due.
• C is the payment amount (each payment is the same amount).
• r is the discount rate or the interest rate per period.
• n is the number of periods.

The formula for the present value of an ordinary annuity is:

PV = C * (1 - 1 / (1 + r)^n)

As you can see, the formula for an annuity due includes an additional term (C / r) that is not present in the formula for an ordinary annuity. This additional term accounts for the fact that the first payment in an annuity due is made immediately, and thus it has a full period of interest to accrue before the next payment is due.