Future Value of an Annuity

An annuity is simply a series of regular cash flows either received or paid periodically.

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

Cash Flow Diagram

The diagram below represents an annuity of 3,000 a period for 3 periods. Notice how each receipt is the same and occurs at the end of each period. This type of annuity is sometimes referred to as a regular annuity or an ordinary annuity.

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

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

Each of the cash flows can be regarded as a single lump sum cash flow and the future value 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 5%, at the end of year 3 the future value of the annuity would be shown as follows:

FV = FV cash flow 1 + FV cash flow 2 + FV cash flow 3 
FV = 3,000 x (1 + 5%)2 + 3,000 x (1 + 5%)1 + 3,000
FV = 9,457.50

The cash flow received at the end of year 1 is compounded forward 2 years to the end of year 3, likewise the cash flow received at the end of year 2 is compounded forward 1 year to the end of year 3, and finally the cash flow received at the end of year 3 does not need compounding as its value is already at 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 is given by the formula

FV = Pmt x ( (1 + i)n - 1 ) / i
Variables used in the formula
FV = Future Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods

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

Pmt = 3,000
i = 5%
n = 3
Future value of an annuity = Pmt x ( (1 + i)n - 1 ) / i
Future value of an annuity = 3,000 x ( (1 + 5%)3 - 1 ) / 5%
Future value of an annuity = 9,457.50

Additional Resources

The future value of annuity 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 March 14th, 2017Team

You May Also Like

Related pages

debit credit chartjournal entry for stock splitthe normal balance of the accumulated depreciation account is debitdeclare cash dividend journal entryaccrued expenseis accumulated depreciation a liabilityprepayment journal entriesis prepaid insurance an asset or liabilityaccounting formula cheat sheetlinear depreciation calculatorwhat is manufacturing overheadhow to calculate inventory turnover periodrules of double entry bookkeepingincreasing annuitypresent value future value formulafifo chartdiscount allowed journal entryledger samplessample inventory sheet exceldefinition of unearned revenuebank reconciliation statement problemsbills receivablesis bad debt expense on income statementformula for future value of annuity duefuture value lump sum formuladepreciation calculation formulapresent value of annuity calculationjournal entry for accrued rentwhat is acid test ratio formulaadjusting entry for unearned revenuerate volume variancecalculating perpetuityformula for degree of operating leverageigcse accounting worksheetsassets equals liabilities plus equityaccounts receivable entriesoverheads in accountingmcq questions on accountingpv of annuity tablethe journal entries for a bank reconciliationdouble declining balance method calculatorbeginning inventory purchasesdeclared dividend journal entryexcel balance sheet formuladepreciation definition wikipediaformula leverage ratioamortisation meaning in accountingmanufacturing overhead journal entryaccounts receivable questions and answerstreasury stock contra equitycalculating quick ratio from balance sheethow to perform vertical analysisdiscounted cash flow excel formulanet credit sales formuladouble bookkeepingsales invoice double entryprepayment balance sheetoutstanding salary journal entrycalculate quick ratio formulaeft electronic funds transfer definitiongross margin excel formulaincome statement balance sheet cash flow template excelfinance lease accounting example lesseereorder point and safety stockjournal entry for accrualledger examplesdeffered revenue expendituremarkup and margin in accountingprovision for bad and doubtful debts entryliquidating a partnershipexcel npv calculatoraverage roavertical analysis of financial statements exampleadjusting entries for interesthow to calculate activity based costingowners equity accounting