Annuity Due

Definition

An annuity due is a financial product where payments are scheduled at the beginning of each period. These periods could be monthly, quarterly, or annually, depending on the contract terms. This differs from the more common ordinary annuity where payments occur at the end of the period.

Examples

1. Rent Payments: Monthly rent payments made at the start of each month are an example of an annuity due.

2. Insurance Premiums: Some insurance policies require premiums to be paid at the start of the coverage period, fitting the description of an annuity due.

3. Lease Agreements: Payments for leased equipment made at the beginning of each leasing period can also be classified as an annuity due.

Frequently Asked Questions (FAQ)

What is the primary difference between an annuity due and an ordinary annuity?

Annuity Due: Payments are made at the beginning of each period. Ordinary Annuity: Payments are made at the end of each period.

Why is the future value of an annuity due higher than that of an ordinary annuity?

Because payments in an annuity due are made at the beginning of each period, each payment has an extra period to accrue interest, resulting in a higher future value.

In which situations would an annuity due be more beneficial?

An annuity due is more beneficial in scenarios where earlier payments yield advantages, such as lower borrowing costs or accruing more interest over time. Examples include lease payments, certain loans, and retirement savings plans.

How is the present value of an annuity due calculated?

The present value of an annuity due is calculated using the formula:

\[ PV = PMT \times \left(1 - (1 + r)^{-n}\right) \times (1 + r) / r \]

where:

• PV = Present Value
• PMT = Payment per period
• r = Periodic interest rate
• n = Number of periods

Can you convert an ordinary annuity to an annuity due?

Yes, conversion is possible by adjusting the timing of the payments. Financial formulas can also be modified by multiplying or dividing by \((1 + r)\) where \( r \) is the interest rate.

Do annuity due payments always have to be fixed?

Most annuity due payments are fixed; however, there are variable annuities that allow the payment amount to vary based on the performance of certain investments.

Related Terms

Ordinary Annuity

An ordinary annuity is a financial product where payments are made at the end of each period.

Perpetuity

A perpetuity is a type of annuity that continues indefinitely, with no end date.

Time Value of Money

The concept that money available now is worth more than the same amount in the future due to its earning potential.

Present Value

The current value of a future sum of money or stream of cash flows, discounted at a specific rate.

Future Value

The value of a current asset at a future date based on an assumed rate of growth over time.

Online References

• Investopedia - Annuity Due
• Wikipedia - Annuity

Suggested Books for Further Studies

1. “Annuities For Dummies” by Kerry Pechter - This book offers a thorough introduction and guidance on various types of annuities.
2. “Valuation of Annuities and Pensions: Basic Interest and Life Contingencies” by S. David Promislow - Detailed examination of annuities, their valuations, and their applications.
3. “The Complete Guide to Annuities” by Matthew Ginnamon CFP - Comprehensive guide focusing on the principles and applications of annuities in financial planning.
4. “Finance: Applications and Theory” by Cornett, Adair, and Nofsinger - This textbook provides in-depth coverage of financial theories, including annuities.

Fundamentals of Annuity Due: Finance Basics Quiz

### What is the main characteristic of an annuity due? - [ ] Payments are made at random intervals. - [ ] Payments are made semi-annually. - [x] Payments are made at the beginning of each period. - [ ] Payments are made at the end of each period. > **Explanation:** The defining feature of an annuity due is that payments are made at the beginning of each period. ### Which has a higher future value: an annuity due or an ordinary annuity? - [x] An annuity due - [ ] An ordinary annuity - [ ] They both have the same future value. - [ ] It depends on the interest rate. > **Explanation:** An annuity due has a higher future value because each payment has an additional period to accrue interest compared to an ordinary annuity. ### Which of the following is an example of an annuity due? - [ ] Monthly rent payments made at the end of each month. - [ ] Annual bond payments received at the end of each year. - [x] Insurance premiums paid at the start of the coverage period. - [ ] Quarterly interest payments on a bond. > **Explanation:** Payments made at the start of each period, such as insurance premiums at the start of the coverage period, are examples of annuity due. ### How is the present value of an annuity due calculated differently from an ordinary annuity? - [ ] By doubling the payment per period. - [ ] By halving the payment per period. - [x] By multiplying by (1 + r). - [ ] By adjusting the payment frequency. > **Explanation:** The present value of an annuity due is calculated by multiplying the ordinary annuity present value by (1 + r), where r is the periodic interest rate. ### Which type of payment period is characteristic of leases and rent payments? - [x] Annuity due - [ ] Ordinary annuity - [ ] Perpetuity - [ ] Lump-sum > **Explanation:** Leases and rent payments typically fall under the category of an annuity due since they are made at the beginning of each period. ### Why can annuity due payments result in more interest accrued over time? - [x] Because payments are made earlier. - [ ] Because payments are made later. - [ ] Because the interest rate is higher. - [ ] Because payments are variable. > **Explanation:** Annuity due payments accrue more interest over time because each payment is made at the beginning of the period, providing more time for the amount to grow. ### What should be multiplied by (1 + r) to obtain the present value of an annuity due? - [ ] The future value - [ ] The lump sum - [x] The ordinary annuity present value - [ ] The periodic payment > **Explanation:** The present value of an annuity due is obtained by multiplying the ordinary annuity present value by (1 + r). ### Annuity due is most advantageous in which scenario? - [ ] When payments are minimal. - [x] When early payments offer more financial benefits. - [ ] When the interest rates are fixed. - [ ] When the payments are high. > **Explanation:** An annuity due is most advantageous when early payments offer more financial benefits, such as lower borrowing costs or greater interest accumulation. ### Which financial product involves payments made at the end of each period? - [ ] Annuity due - [x] Ordinary annuity - [ ] Immediate annuity - [ ] Deferred annuity > **Explanation:** An ordinary annuity involves payments made at the end of each period, in contrast to an annuity due where payments are made at the beginning. ### Can ordinary annuity payments be converted to annuity due payments, and how? - [ ] No, it's not possible. - [x] Yes, by adjusting the timing and interest calculations. - [ ] Yes, by doubling the interest rate. - [ ] No, but annuity due can be converted to ordinary annuity. > **Explanation:** Ordinary annuity payments can be converted to annuity due payments by adjusting the timing of payments and applying the appropriate financial formulas to account for the difference in timing.

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