An annuity due is a type of financial arrangement where a series of equal payments or receipts are made at the beginning of each period, rather than at the end. The term “annuity” refers to a stream of payments or receipts that occur at regular intervals. When these payments occur at the beginning of each period, it is called an “annuity due.”

Here are some key points about annuities due:

1. **Payment Timing:**

– In an ordinary annuity, payments are made or received at the end of each period. In contrast, with an annuity due, the payments are made or received at the beginning of each period.

2. **Mathematical Representation:**

– The present value and future value formulas for annuities due are slightly different from those for ordinary annuities. The adjustment is made to account for the fact that cash flows are occurring at the beginning of each period.

– For the present value of an annuity due, you would typically multiply the ordinary annuity formula by (1 + r), where “r” is the interest rate per period.

– For the future value of an annuity due, you would typically multiply the ordinary annuity formula by (1 + r), where “r” is the interest rate per period.

3. **Examples:**

– Rent payments, lease payments, and certain types of insurance premiums are examples of annuities due because they are typically paid at the beginning of the rental, lease, or coverage period.

4. **Comparison with Ordinary Annuities:**

– The key difference between an annuity due and an ordinary annuity is the timing of cash flows. In an ordinary annuity, payments occur at the end of each period, while in an annuity due, payments occur at the beginning.

5. **Time Value of Money:**

– Annuities due take into account the time value of money, recognizing that a payment received or made today has a different value than the same payment in the future.

6. **Calculations:**

– Calculating the present value and future value of an annuity due requires specific formulas that adjust for the timing of cash flows. These calculations involve incorporating the interest rate and the timing of payments.

Understanding the timing of cash flows is crucial when working with financial calculations, especially when dealing with annuities. Whether an annuity is ordinary or due can impact the overall value of the cash flows and the financial decision-making process.