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PV of Beginning of Period Annuities over n years = A + A

This present value will be higher than the present value of an equivalent annuity at the end of each period.

The future value of a beginning-of-the-period annuity typically can be estimated by allowing for one additional period of compounding for each cash flow:

FVof a Beginning - of - the - Period Annuity = A (1+r)

This future value will be higher than the future value of an equivalent annuity at the end of each period.

Consider again the example of an individual who sets aside $2,000 at the end of each year for the next 40 years in an IRA account at 8%. The future value of these deposits amounted to $ 518,113 at the end of year 40. If the deposits had been made at the beginning of each year instead of the end, the future value would have been higher:

Expected Value of IRA (beginning of year) = $2,000 (1.08)

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