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Present Value of Growing Annuity Formula

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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. Check FAQs

PV ga = (\frac{II}{r - g}) \cdot (1 - {(\frac{1 + g}{1 + r})}^{n Periods})

PV_ga - Present Value of Growing Annuity?II - Initial Investment?r - Rate per Period?g - Growth Rate?n_Periods - Number of Periods?

Present Value of Growing Annuity Example

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Here is how the Present Value of Growing Annuity equation looks like with Values.

Here is how the Present Value of Growing Annuity equation looks like with Units.

Here is how the Present Value of Growing Annuity equation looks like.

3755.102 = (\frac{2000}{0.05 - 0.02}) \cdot (1 - {(\frac{1 + 0.02}{1 + 0.05})}^{2})

3755.102 = (\frac{2000}{0.05 - 0.02}) \cdot (1 - {(\frac{1 + 0.02}{1 + 0.05})}^{2})

3755.102 = (\frac{2000}{0.05 - 0.02}) \cdot (1 - {(\frac{1 + 0.02}{1 + 0.05})}^{2})

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Present Value of Growing Annuity Solution

Follow our step by step solution on how to calculate Present Value of Growing Annuity?

FIRST Step Consider the formula

PV ga = (\frac{II}{r - g}) \cdot (1 - {(\frac{1 + g}{1 + r})}^{n Periods})

Next Step Substitute values of Variables

∴

PV ga = (\frac{2000}{0.05 - 0.02}) \cdot (1 - {(\frac{1 + 0.02}{1 + 0.05})}^{2})

Next Step Prepare to Evaluate

∴

PV ga = (\frac{2000}{0.05 - 0.02}) \cdot (1 - {(\frac{1 + 0.02}{1 + 0.05})}^{2})

Next Step Evaluate

∴

PV ga = 3755.10204081633

LAST Step Rounding Answer

∴

PV ga = 3755.102

Present Value of Growing Annuity Formula Elements

Variables

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.

Symbol: PV_ga

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Present Value of Growing Annuity

Initial Investment

The Initial Investment is the amount required to start a business or a project.

Symbol: II

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Initial Investment

Rate per Period

The Rate per Period is the interest rate charged.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Rate per Period

Growth Rate

Growth Rate refer to the percentage change of a specific variable within a specific time period, given a certain context.

Symbol: g

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Growth Rate

Number of Periods

The Number of Periods is the periods on an annuity using the present value, periodic payment, and periodic rate.

Symbol: n_Periods

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Periods

Other formulas in Present Value category

Go Present Value of Annuity

PVAnnuity = (\frac{p}{IR}) \cdot (1 - (\frac{1}{{(1 + IR)}^{n Months}}))

Go Present Value of Future Sum given compounding periods

PV = \frac{FV}{{(1 + (\frac{%RoR}{C n}))}^{C n \cdot n Periods}}

Go Present Value of Future Sum given Total Number of Periods

PV = \frac{FV}{{(1 + IR)}^{t}}

Go Present Value of Future Sum given Number of Periods

PV = \frac{FV}{\exp (%RoR \cdot n Periods)}

How to Evaluate Present Value of Growing Annuity?

Present Value of Growing Annuity evaluator 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 evaluate 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 evaluate Present Value of Growing Annuity using this online evaluator? To use this online evaluator 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.

FAQs on Present Value of Growing Annuity

What is the formula to find Present Value of Growing Annuity?

The formula of Present Value of Growing Annuity is expressed as Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods)). Here is an example- 4081.633 = (2000/(0.05-0.02))*(1-((1+0.02)/(1+0.05))^(2)).

How to calculate Present Value of Growing Annuity?

With Initial Investment (II), Rate per Period (r), Growth Rate (g) & Number of Periods (n_Periods) we can find Present Value of Growing Annuity using the formula - Present Value of Growing Annuity = (Initial Investment/(Rate per Period-Growth Rate))*(1-((1+Growth Rate)/(1+Rate per Period))^(Number of Periods)).

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Present Value of Growing Annuity Formula

Present Value of Growing Annuity Example

Present Value of Growing Annuity Solution

Present Value of Growing Annuity Formula Elements

Other formulas in Present Value category

How to Evaluate Present Value of Growing Annuity?

FAQs on Present Value of Growing Annuity

Variable Name