Growing Annuity Payment Formula PV


Pmt = PV x (i - g) / (1 - (1 + g)n x (1 + i)-n )
Variables used in the growing annuity payment formula PV
PV = Present Value
Pmt = Initial payment at the end of period one
i = Discount rate
n = Number of periods
g = Growth rate


This growing annuity payment formula PV calculates the initial annuity payment required to provide a given value today PV (present value) using a growing annuity. The growing annuity payment formula assumes payments are made at the end of each period for n periods and are growing or declining at a constant rate g, and a discount rate i is applied.

Example Using Growing Annuity Payment Formula PV

Initial Payment

The initial payment is made at the end of period one. Suppose an investment provides 12 (n) regular periodic payments growing at a rate of 2% (g) each period. Assuming a discount rate of 5% (i), and a required present value of 5,000 (PV), what is the amount of the first (initial) payment required.

The initial payment amount is given by the growing annuity payment formula PV as follows:

Pmt = PV x (i - g) / (1 - (1 + g)n x (1 + i)-n )
Pmt = 5,000 x (5% - 2%) / (1 - (1 + 2%)12 x (1 + 5%)-12 )
Pmt = 510.56

Later Period Payments

The initial payment calculated above is made at the end of period one. The value of the payment at the end of any other period is calculated by compounding the initial payment forward at the growth rate (g) using the future value of a single payment formula. For example, if the amount of the payment at the end of period nine is required, then this would be calculated as follows:

FV = PV x (1 + i)n
FV = Pmt (9)
PV = Pmt (1)
n = 8 (periods between 1 and 9)
Pmt(n) = Pmt(1) x (1 + g)n
Pmt(9) = 510.56 x (1 + 2%)8
Pmt(9) = 598.20

At a growth rate of 2% (g), the initial payment at the end of period one of 510.56, would have grown into a payment 598.20 by the end of period nine.

The growing annuity payment formula PV is one of many growing annuity formulas used in time value of money calculations, discover another at the link below.

Growing Annuity Payment Formula PV November 6th, 2016Team

You May Also Like

Related pages

overhead absorption costingaccrude expensefuture value annuity factor formulaformula gearing ratioaccounts payable turnover calculatorpetty cash floatending inventory calculatordouble entry accounting principleshow to compute contribution margin ratiohow to calculate depreciation rate for reducing balance methodpmt excel functionpresent value table annuitycalculating the present value of an annuityannuity due calculatoraccumulated depreciation contra assetgaap chart of accounts standardhow to record fixed assets in quickbooksdupont roe calculatorrestaurant chart of accounts examplecash flow statement retained earningsbookkeeping templateaccounting turnover formulahow to calculate inventory variancewhat is sunk cost in accountingmanufacturing overheadsjournal entry for issuing stockaccounts receivable entrieshow to calculate stock turnover dayshow to calculate purchase price varianceliquidity acid testretail bookkeepingcapital lease journal entriesdiscount factor formula excelpetty cash report formathow to calculate markup costperpetual method of inventoryprepaid rent journal entryamortization table for bondsledger samplelong term notes payable journal entryhow to calculate inventory turnover ratioarr calculatorledger balance templatevertical profit and loss account format in excelwhat does sundry expenses meanbank reconciliation statement pdf notesdays debtors ratiohow to use irr function in excelprofitablility indexaccounts receivable days outstanding formulaconvertible participating preferredcalculating double declining depreciationintro to accounting quizexample of prepaid expensesremittance accountingexamples of accrued revenuesimple gross margin calculatoraccount receivable days formularetail markup formulatransposition error in accountingdupont return on assetsebit interest coverage ratiodouble entry of depreciationformula for working capital turnover ratiohow to calculate stockholders equityis allowance for doubtful accounts a debit or creditgaap chart of accounts numberingtotal gearing ratiounpaid balance calculatorgross profit calculation examplecash basis bookkeepingcredit sales in income statementbudgeted overheadfactoring receivable