October 15, 2023

## Getting Started

When it comes to financial planning and investment strategies, annuities play an important role in providing a steady stream of income during retirement or for a predetermined period of time. Annuities are essentially a series of periodic payments made to an individual or entity in exchange for a lump sum investment. However, there are two types of annuities: ordinary annuities and annuity riders. In this article, we will examine the reasons why an annuity due is higher than an ordinary annuity and explore the factors that contribute to this difference.

## Understanding Annuity Due

An annuity due is a type of annuity in which the cash flow payments are made at the beginning of each period rather than at the end. In other words, the payments are made in advance. This key difference distinguishes an annuity due from a regular annuity, where payments are made at the end of each period. The timing of the payments has a significant impact on the overall value of the annuity and the income it generates.

## Time Value of Money

One of the basic concepts that helps explain why the annuity payable is higher than a regular annuity is the time value of money. The time value of money recognizes that the value of money changes over time due to various factors such as inflation and the opportunity cost of investing funds elsewhere. When cash flows are received earlier, as in the case of an annuity, the investor has the opportunity to reinvest those funds and earn additional returns.

Consider a scenario where two individuals, John and Sarah, invest the same amount of money in annuities with the same interest rate. John chooses a regular annuity, while Sarah chooses an immediate annuity. Because Sarah receives her payments at the beginning of each period, she can invest those funds immediately, potentially earning additional interest. This compounding effect results in a higher total value for the immediate annuity than for the simple annuity.

## PV Calculation and Discounting

The calculation of present value (PV) is another factor that contributes to the difference between the annuity payable and the ordinary annuity. PV is used to determine the present value of future cash flows by discounting them back to the present using an appropriate discount rate. The timing of the cash flows affects the discounting process and therefore the present value.

In the case of an annuity, because the cash flows occur at the beginning of each period, they are discounted for a shorter period than for an ordinary annuity. This shorter discounting period results in a lower discount rate and therefore a higher present value for the annuity due. On the other hand, the ordinary annuity discounts the cash flows for a longer period, resulting in a higher discount factor and a lower present value.

## Risk and Cash Flow Timing

The timing of cash flows also has implications for risk and the opportunity cost of money. An annuity provides an advantage by ensuring earlier receipt of cash flows. This can be particularly beneficial when there is uncertainty or risk associated with future payments. By receiving payments in advance, the annuity due investor can reduce the risk of default or non-payment in the future.

In addition, the earlier cash flows from the annuity due can provide the investor with flexibility and liquidity. They can be used for a variety of purposes, including meeting immediate expenses, reinvesting in other opportunities, or simply providing peace of mind. This added flexibility and reduced risk contribute to the higher value and attractiveness of an annuity due compared to a regular annuity.

## Conclusion

In summary, the annuity due is higher than the ordinary annuity due to several key factors. The time value of money recognizes the potential for additional returns when cash flows are received earlier, resulting in a higher overall value. The PV calculation and discounting process also favor the annuity due, resulting in a higher present value. In addition, the reduced risk and increased flexibility associated with the annuity due makes it more attractive to investors. Understanding these factors is critical for individuals seeking to make informed decisions about their retirement planning and investment strategies.

## FAQs

### Why is annuity due higher than ordinary annuity?

An annuity due is higher than an ordinary annuity due to the timing of the cash flows. In an ordinary annuity, the periodic payments are made at the end of each period, while in an annuity due, the payments are made at the beginning of each period. This difference in timing affects the present value of the cash flows and leads to a higher value for the annuity due.

### How does the timing of cash flows affect the value of annuity due?

The timing of cash flows affects the value of an annuity due because receiving payments at the beginning of each period allows the investor to earn interest on those funds for an additional period. This means that the present value of the cash flows in an annuity due is higher compared to an ordinary annuity, where payments are made at the end of each period.

### What is the formula for calculating the future value of an annuity due?

The formula for calculating the future value of an annuity due is FV = P * (1 + r) * ((1 + r)^n – 1) / r, where FV is the future value, P is the periodic payment, r is the interest rate per period, and n is the number of periods.

### What is the formula for calculating the present value of an annuity due?

The formula for calculating the present value of an annuity due is PV = P * (1 – (1 + r)^(-n)) / r, where PV is the present value, P is the periodic payment, r is the interest rate per period, and n is the number of periods.

### Can you provide an example to illustrate the difference between annuity due and ordinary annuity?

Sure! Let’s consider an example where you have two annuities, one ordinary annuity and one annuity due. Both annuities have a payment of \$1000 per month, an interest rate of 5% per year, and a duration of 10 years.

For the ordinary annuity, the payments are made at the end of each month, so the future value would be calculated as FV = 1000 * (1 + 0.05/12)^(12*10) – 1 / (0.05/12), resulting in a future value of approximately \$155,222.82.

For the annuity due, the payments are made at the beginning of each month, so the future value would be calculated as FV = 1000 * (1 + 0.05/12) * ((1 + 0.05/12)^(12*10) – 1) / (0.05/12), resulting in a future value of approximately \$162,854.35.

As you can see, the annuity due has a higher future value compared to the ordinary annuity due to the additional interest earned by receiving payments at the beginning of each period.