## Growing Annuity Payment using Present Value Solution

STEP 0: Pre-Calculation Summary
Formula Used
Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods)))
PMTinitial = PV*((r-g)/(1-(((1+g)/(1+r))^nPeriods)))
This formula uses 5 Variables
Variables Used
Initial Payment - Initial Payment refers to the first installment or upfront amount paid at the beginning of a financial transaction or contract.
Present Value - The Present Value of the annuity is the value that determines the value of a series of future periodic payments at a given time.
Rate per Period - The Rate per Period is the interest rate charged.
Growth Rate - Growth Rate refer to the percentage change of a specific variable within a specific time period, given a certain context.
Number of Periods - The Number of Periods is the periods on an annuity using the present value, periodic payment, and periodic rate.
STEP 1: Convert Input(s) to Base Unit
Present Value: 100 --> No Conversion Required
Rate per Period: 0.05 --> No Conversion Required
Growth Rate: 0.02 --> No Conversion Required
Number of Periods: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PMTinitial = PV*((r-g)/(1-(((1+g)/(1+r))^nPeriods))) --> 100*((0.05-0.02)/(1-(((1+0.02)/(1+0.05))^2)))
Evaluating ... ...
PMTinitial = 53.2608695652174
STEP 3: Convert Result to Output's Unit
53.2608695652174 --> No Conversion Required
53.2608695652174 53.26087 <-- Initial Payment
(Calculation completed in 00.004 seconds)
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## Credits

Created by Keerthika Bathula
Indian Institute of Technology, Indian School of mines, Dhanbad (IIT ISM Dhanbad), Dhanbad
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## < 19 Present value Calculators

Present Value of Deferred Annuity
Present Value of Deferred Annuity = Ordinary Annuity Payment*(1-(1+(Interest Rate*0.01))^-Number of Periods)/((1+(Interest Rate*0.01)^Deferred Periods*(Interest Rate*0.01)))
Present Value of Deferred Annuity based on Annuity Due
Present Value of Deferred Annuity = Annuity Payment Due*(1-(1+(Interest Rate*0.01))^-Number of Periods)/((1+(Interest Rate*0.01))^(Deferred Periods-1)*(Interest Rate*0.01))
Present Value of Growing Annuity
Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods))
Growing Annuity Payment using Present Value
Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods)))
Annuity Due for Present Value
Annuity Due Present Value = Payment made in Each Period*((1-(1/(1+Rate per Period)^(Number of Periods)))/Rate per Period)*(1+Rate per Period)
Present Value of Future Sum given compounding periods
Present Value = Future Value/(1+(Rate of Return/Compounding Periods))^(Compounding Periods*Number of Periods)
Number of Periods using Present Value of Annuity
Total Number of Periods = ln((1-(Present Value of Annuity/Cashflow per Period))^-1)/ln(1+Rate per Period)
Present Value of Ordinary Annuities and Amortization
Present Value = Payment made in Each Period*((1-(1+Rate per Period)^(-Total Number of Times Compounded))/Rate per Period)
Present Value of Annuity with Continuous Compounding
Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1))
Present Value of Annuity
Present Value of Annuity = (Monthly Payment/Interest Rate)*(1-(1/(1+Interest Rate)^Number of Months))
Present Value of Future Sum given Number of Periods
Present Value = Future Value/exp(Rate of Return*Number of Periods)
Present Value for Continuous Compounding
Present Value with Continuous Compounding = Future Value/(e^(Rate per Period*Number of Periods))
Present Value Factor
Annuity Present Value Factor = (1-((1+Rate per Period)^(-Number of Periods)))/Rate per Period
Present Value of Stock with Constant Growth
Price of Stock = Estimated Dividends for Next Period/((Rate of Return*0.01)-Growth Rate)
Present Value of Lumpsum
Present Value of Lumpsum = Future Value/(1+Interest Rate per Period)^Number of Periods
Present Value of Future Sum given Total Number of Periods
Present Value = Future Value/(1+Interest Rate)^Total Number of Periods
Present Value Continuous Compounding Factor
PV Continuous Compounding Factor = (e^(-Rate per Period*Total Number of Periods))
PV of Perpetuity
PV of Perpetuity = Dividend/Discount Rate
Present Value of Stock with Zero Growth
Price of Stock = Dividend/Rate of Return

## Growing Annuity Payment using Present Value Formula

Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods)))
PMTinitial = PV*((r-g)/(1-(((1+g)/(1+r))^nPeriods)))

## What is Growing Annuity Payment using Present Value?

A growing annuity payment using present value refers to a series of periodic payments that increase over time and are adjusted for inflation or growth, all while taking into account the time value of money. This concept is particularly relevant in finance and investment planning, where future cash flows are discounted to their present value. The growing annuity payment accounts for factors such as rising costs or increasing income, ensuring that the payments maintain their purchasing power or grow in line with expected earnings. By calculating the present value of these growing annuity payments, individuals and businesses can make informed decisions about long-term financial commitments, retirement planning, and investment strategies, considering the impact of inflation and changing economic conditions.

## How to Calculate Growing Annuity Payment using Present Value?

Growing Annuity Payment using Present Value calculator uses Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods))) to calculate the Initial Payment, The Growing Annuity Payment using Present Value is the increasing series of periodic payments, adjusted for inflation or growth, that equate to a specified present value considering the time value of money. Initial Payment is denoted by PMTinitial symbol.

How to calculate Growing Annuity Payment using Present Value using this online calculator? To use this online calculator for Growing Annuity Payment using Present Value, enter Present Value (PV), Rate per Period (r), Growth Rate (g) & Number of Periods (nPeriods) and hit the calculate button. Here is how the Growing Annuity Payment using Present Value calculation can be explained with given input values -> 53.26087 = 100*((0.05-0.02)/(1-(((1+0.02)/(1+0.05))^2))).

### FAQ

What is Growing Annuity Payment using Present Value?
The Growing Annuity Payment using Present Value is the increasing series of periodic payments, adjusted for inflation or growth, that equate to a specified present value considering the time value of money and is represented as PMTinitial = PV*((r-g)/(1-(((1+g)/(1+r))^nPeriods))) or Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods))). The Present Value of the annuity is the value that determines the value of a series of future periodic payments at a given time, The Rate per Period is the interest rate charged, Growth Rate refer to the percentage change of a specific variable within a specific time period, given a certain context & The Number of Periods is the periods on an annuity using the present value, periodic payment, and periodic rate.
How to calculate Growing Annuity Payment using Present Value?
The Growing Annuity Payment using Present Value is the increasing series of periodic payments, adjusted for inflation or growth, that equate to a specified present value considering the time value of money is calculated using Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods))). To calculate Growing Annuity Payment using Present Value, you need Present Value (PV), Rate per Period (r), Growth Rate (g) & Number of Periods (nPeriods). With our tool, you need to enter the respective value for Present Value, Rate per Period, Growth Rate & Number of Periods and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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