Future Value of an Annuity Due

An annuity is simply a series of regular cash flows either received or paid periodically. An annuity due is one in which the cash flows occur at the beginning of each period.

Life insurance, pension payments, motor vehicle leases, property rents, are all forms of annuities.

Cash Flow Diagram

The diagram below represents an annuity due of 4,000 a period for 3 periods. Notice how each receipt is the same and occurs at the beginning of each period. This is in contrast to an ordinary annuity where the cash flows occur at the end of a period.

Future value of an annuity due cash flow diagram
Period 0 1 2 3
Cash flow ↑ 4,000 ↑ 4,000 ↑ 4,000

The period for an annuity can be of any length, week, month year etc. providing all periods are of the same length.

Future Value of an Annuity Due

Each of the cash flows can be regarded as a single lump sum cash flow and the future value of an annuity due can be calculated using the future value of a lump sum formula, by compounding each cash flow forward to the end of year 3.

In the above example, assuming a periodic discount rate of 6%, at the end of year 3 the future value of an annuity due would be shown as follows:

```FV = FV cash flow 1 + FV cash flow 2 + FV cash flow 3
FV = 4,000 x (1 + 6%)3 + 4,000 x (1 + 6%)2 + 4,000 x (1 + 6%)1
FV = 13,498.46
```

The cash flow received at the beginning of year 1 is compounded forward 3 years to the end of year 3, likewise the cash flow received at the beginning of year 2 is compounded forward 2 years to the end of year 3, and finally the cash flow received at the beginning of year 3 is compounded forward 1 year to the end of year 3.

Clearly this calculation can be performed for any number of periods and cash flows, however to avoid repetitive time, consuming calculations, it can be shown mathematically that the future value of an annuity due is given by the formula

`FV = Pmt x (1 + i) x ( (1 + i)n - 1 ) / i`
Variables used in the formula
FV = future value of an annuity due
Pmt = Periodic payment
i = Discount rate
n = Number of periods

It should be noted that, rearranged, this formula is simply the formula for the future value of an ordinary annuity (highlighted in red), compounded forward one more period by the term (1 + i).

`FV = (1 + i) x Pmt x ( (1 + i)n - 1 ) / i`

This results from the fact that for an annuity due the cash flows occur at the beginning of the period, one period earlier than those of an ordinary annuity, and so one additional period of compounding takes place.

Using the above annuity due as an example, the future value of the annuity due at the end of year 3 can be calculated using the formula as follows:

```Pmt = 4,000
i = 6%
n = 3
FV = Pmt x (1 + i) x ( (1 + i)n - 1 ) / i
FV = 4,000 x (1 + 6%) x ( (1 + 6%)3 - 1 ) / 6%
FV = 13,498.46
```

The future value of annuity due forms the basis of many time value of money calculations. The formula allows any series of regular cash flows (Pmt) to be compounded forward a number of periods (n) at a discount rate of i per period.

Future Value of an Annuity Due November 6th, 2016

Related pages

high degree of operating leveragecauses of labour rate variancesample money receipt formatprocess costing fifopetty cash analysis sheetrule 78 calculatorjournal entries for trading securitiesdebt equity ratio calculation formulatotal monthly fixed manufacturing costformat of receipt voucherimprest system petty cashobsolete inventory definitionaccounts payable skills testfactoring accountingsteps of the accounting cyclecreditor ratiocommon size analysis of income statementwhat is double entry bookkeepingaccounting formula assets liabilitiesnet present value of annuity calculatorhow to calculate inventory turnover ratiogordon growth model excelgross profit calcdepreciation accumulated depreciation journal entrypresent value of annuitiesperiodic interest rate calculatorprovision for doubtful accounts journal entrynote payable journal entrygrowing annuity present valueaccounting eqautionincome statement periodic inventory systemhow to find future value of annuityselling goods on consignmentadjusting entries inventoryinterest on investment journal entryadvantages and disadvantages of accounting rate of returncredits and debits for dummiesformula for horizontal analysisexcel present value calculatorcogs formula income statementdirect labour cost varianceannual depreciation straight line methodpresent value of an annuity in exceladvantages and disadvantages of pay back periodpresent value tables annuityis unearned revenue an assetconsignee sales agentfuture value of annuity charthow to calculate the contribution margindupont return on equityaccounting for allowance for doubtful accountsaccounts receivable control ledgerdebtors days calculation formuladiscounting cash flows in excelpetty cash receipt templatecash dividend declaredjournal entry for writing off accounts receivablehow to calculate present value annuitymeaning of eomfv tablesproforma of trial balanceppe fixed assetsear finance formulawhat does single entry accounting meanobsolescence accountingwhat are consumable suppliesexcel pmt functionpreparation of petty cash bookwhat is the meaning of retained earningshow to record depreciation expense journal entrycash disbursement bookannuity table pdfpremium bonds payablemeaning of imprest money