Growing Annuity Payment using Present Value Calculator

✖The Present Value of the annuity is the value that determines the value of a series of future periodic payments at a given time.ⓘ Present Value [PV]			+10% -10%
✖The Rate per Period is the interest rate charged.ⓘ Rate per Period [r]			+10% -10%
✖Growth Rate refer to the percentage change of a specific variable within a specific time period, given a certain context.ⓘ Growth Rate [g]			+10% -10%
✖The Number of Periods is the periods on an annuity using the present value, periodic payment, and periodic rate.ⓘ Number of Periods [n_Periods]			+10% -10%

✖Initial Payment refers to the first installment or upfront amount paid at the beginning of a financial transaction or contract.ⓘ Growing Annuity Payment using Present Value [PMT_initial]

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Formula

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Growing Annuity Payment using Present Value

Formula

`"PMT"_{"initial"} = "PV"*(("r"-"g")/(1-(((1+"g")/(1+"r"))^"n"_{"Periods"})))`

Example

`"53.26087"="100"*(("0.05"-"0.02")/(1-(((1+"0.02")/(1+"0.05"))^"2")))`

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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)))
PMT_initial = PV*((r-g)/(1-(((1+g)/(1+r))^n_Periods)))
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

PMT_initial = PV*((r-g)/(1-(((1+g)/(1+r))^n_Periods))) --> 100*((0.05-0.02)/(1-(((1+0.02)/(1+0.05))^2)))

Evaluating ... ...

PMT_initial = 53.2608695652174

STEP 3: Convert Result to Output's Unit

53.2608695652174 --> No Conversion Required

FINAL ANSWER

53.2608695652174 ≈ 53.26087 <-- Initial Payment

(Calculation completed in 00.004 seconds)

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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

Go 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

Go 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

Go 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

Go 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

Go 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

Go Present Value = Future Value/(1+(Rate of Return/Compounding Periods))^(Compounding Periods*Number of Periods)

Number of Periods using Present Value of Annuity

Go 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

Go 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

Go Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1))

Present Value of Annuity

Go 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

Go Present Value = Future Value/exp(Rate of Return*Number of Periods)

Present Value for Continuous Compounding

Go Present Value with Continuous Compounding = Future Value/(e^(Rate per Period*Number of Periods))

Present Value Factor

Go Annuity Present Value Factor = (1-((1+Rate per Period)^(-Number of Periods)))/Rate per Period

Present Value of Stock with Constant Growth

Go Price of Stock = Estimated Dividends for Next Period/((Rate of Return*0.01)-Growth Rate)

Present Value of Lumpsum

Go Present Value of Lumpsum = Future Value/(1+Interest Rate per Period)^Number of Periods

Present Value of Future Sum given Total Number of Periods

Go Present Value = Future Value/(1+Interest Rate)^Total Number of Periods

Present Value Continuous Compounding Factor

Go PV Continuous Compounding Factor = (e^(-Rate per Period*Total Number of Periods))

PV of Perpetuity

Go PV of Perpetuity = Dividend/Discount Rate

Present Value of Stock with Zero Growth

Go 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)))
PMT_initial = PV*((r-g)/(1-(((1+g)/(1+r))^n_Periods)))

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 PMT_initial 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 (n_Periods) 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 PMT_initial = PV*((r-g)/(1-(((1+g)/(1+r))^n_Periods))) 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 (n_Periods). 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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