Present Value of Growing Annuity Calculator

✖The Initial Investment is the amount required to start a business or a project.ⓘ Initial Investment [II]			+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%

✖Present Value of Growing Annuity refers to the current worth of a series of cash flows that are expected to increase at a constant rate over time.ⓘ Present Value of Growing Annuity [PV_ga]

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Formula

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Present Value of Growing Annuity

Formula

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

Example

`"3755.102"=("2000"/("0.05"-"0.02"))*(1-((1+"0.02")/(1+"0.05"))^("2"))`

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Present Value of Growing Annuity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods))
PV_ga = (II/(r-g))*(1-((1+g)/(1+r))^(n_Periods))
This formula uses 5 Variables

Variables Used

Present Value of Growing Annuity - Present Value of Growing Annuity refers to the current worth of a series of cash flows that are expected to increase at a constant rate over time.
Initial Investment - The Initial Investment is the amount required to start a business or a project.
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

Initial Investment: 2000 --> 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

PV_ga = (II/(r-g))*(1-((1+g)/(1+r))^(n_Periods)) --> (2000/(0.05-0.02))*(1-((1+0.02)/(1+0.05))^(2))

Evaluating ... ...

PV_ga = 3755.10204081633

STEP 3: Convert Result to Output's Unit

3755.10204081633 --> No Conversion Required

FINAL ANSWER

3755.10204081633 ≈ 3755.102 <-- Present Value of Growing Annuity

(Calculation completed in 00.004 seconds)

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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

Present Value of Growing Annuity Formula

Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods))
PV_ga = (II/(r-g))*(1-((1+g)/(1+r))^(n_Periods))

What is Present Value of Growing Annuity?

The present value of a growing annuity refers to the current worth of a series of cash flows that are expected to increase at a constant rate over time. A growing annuity differs from a regular annuity in that the cash flows increase by a fixed percentage (growth rate) each period.
The formula to calculate the present value of a growing annuity takes into account the increasing nature of the cash flows. It considers both the time value of money (discounting future cash flows back to their present value) and the growth rate of the cash flows.

How to Calculate Present Value of Growing Annuity?

Present Value of Growing Annuity calculator uses Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods)) to calculate the Present Value of Growing Annuity, The Present Value of Growing Annuity formula is defined as the current worth of a series of cash flows that are expected to increase at a constant rate over time. Present Value of Growing Annuity is denoted by PV_ga symbol.

How to calculate Present Value of Growing Annuity using this online calculator? To use this online calculator for Present Value of Growing Annuity, enter Initial Investment (II), Rate per Period (r), Growth Rate (g) & Number of Periods (n_Periods) and hit the calculate button. Here is how the Present Value of Growing Annuity calculation can be explained with given input values -> 4081.633 = (2000/(0.05-0.02))*(1-((1+0.02)/(1+0.05))^(2)).

FAQ

What is Present Value of Growing Annuity?

The Present Value of Growing Annuity formula is defined as the current worth of a series of cash flows that are expected to increase at a constant rate over time and is represented as PV_ga = (II/(r-g))*(1-((1+g)/(1+r))^(n_Periods)) or Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods)). The Initial Investment is the amount required to start a business or a project, 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 Present Value of Growing Annuity?

The Present Value of Growing Annuity formula is defined as the current worth of a series of cash flows that are expected to increase at a constant rate over time is calculated using Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods)). To calculate Present Value of Growing Annuity, you need Initial Investment (II), Rate per Period (r), Growth Rate (g) & Number of Periods (n_Periods). With our tool, you need to enter the respective value for Initial Investment, 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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