Annuities are contracts offered by insurance companies that allow people to secure a steady stream of income when they retire. In exchange for a lump-sum payment, the insurance company agrees to make regular payments back to you over a number of years. Ordinarily those payments begin at the end of the period when you started the annuity. When the annuity begins with a payment, it's called an annuity due.

## Difference in Payout

Annuities make a payment once per period, much like bills are due once per billing cycle. That payment can come either at the end of the period or at the beginning. Ordinary annuities pay out at the end of the cycle after they begin. Annuities due, on the other hand, begin with a payment and continue to pay out at the beginning of each cycle. Insurance premiums, for example, are due at the beginning of each billing cycle as are annuities due. Loan payments, on the other hand, are payable at the end of the cycle, as are ordinary annuities.

## What Does It Change

As a consumer you’re often on the receiving end of pricing decisions based, in part, around a present value of an annuity calculation. Companies use the concept of annuities to calculate how much they need to charge in future payments to make a profit from a current expense. If you make your first payment at the end of the billing cycle, as in an ordinary annuity, your payments need to be larger than if your first payment is due immediately.

## Present Value of an Annuity

Money loses purchasing power over time, so the same amount of money buys less at the end of the year than it does at the beginning of the year. When people want to compare the value of future revenue streams against a single expense, they have to calculate the present value of an annuity. Even the amount of time between the beginning and end of a billing cycle has a significant enough impact on the value of money that you need to know whether the stream of payments comes at the beginning or the end of the cycle to calculate its present value.

## Present Value Factors

You calculate the present value of any annuity by multiplying a present value factor and the size of the periodic payment. With an annuity due, you have the cash for an extra period compared to what you have with an ordinary annuity. The present value factor for an annuity due is simply the factor for an ordinary annuity with an additional period's interest. For example, the present value factor for an ordinary annuity that pays out over five periods at 5 percent interest is 4.32948. Multiplying that by 1.05 provides the present value factor for the same payments as an annuity due, 4.545954.

## The Impact on Pricing

Say a company offers a five-year subscription. Providing the service has a one-time cost per customer of $270. The company wants to make a $1,000 profit from each subscription, so it needs to price the payments accordingly. By dividing $1,270 -- the present value the company wants from the subscription -- by the present value factor, the company arrives at how much it should charge each year. If the company bills at the end of each year, it has to charge more than if it bills up front. For example, it would need to bill $293.34 instead of $279.37.

### References

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