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Growing Annuity Payment using Present Value Formula

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Initial Payment refers to the first installment or upfront amount paid at the beginning of a financial transaction or contract. Check FAQs

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

PMT_initial - Initial Payment?PV - Present Value?r - Rate per Period?g - Growth Rate?n_Periods - Number of Periods?

Growing Annuity Payment using Present Value Example

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

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

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

53.2609 = 100 \cdot (\frac{0.05 - 0.02}{1 - ({(\frac{1 + 0.02}{1 + 0.05})}^{2})})

53.2609 = 100 \cdot (\frac{0.05 - 0.02}{1 - ({(\frac{1 + 0.02}{1 + 0.05})}^{2})})

53.2609 = 100 \cdot (\frac{0.05 - 0.02}{1 - ({(\frac{1 + 0.02}{1 + 0.05})}^{2})})

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Growing Annuity Payment using Present Value Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

PMT initial = 100 \cdot (\frac{0.05 - 0.02}{1 - ({(\frac{1 + 0.02}{1 + 0.05})}^{2})})

Next Step Prepare to Evaluate

∴

PMT initial = 100 \cdot (\frac{0.05 - 0.02}{1 - ({(\frac{1 + 0.02}{1 + 0.05})}^{2})})

Next Step Evaluate

∴

PMT initial = 53.2608695652174

LAST Step Rounding Answer

∴

PMT initial = 53.2609

Growing Annuity Payment using Present Value Formula Elements

Variables

Initial Payment

Initial Payment refers to the first installment or upfront amount paid at the beginning of a financial transaction or contract.

Symbol: PMT_initial

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Initial Payment

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.

Symbol: PV

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Present Value

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 Growing Annuity Payment using Present Value?

Growing Annuity Payment using Present Value evaluator uses Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods))) to evaluate 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 evaluate Growing Annuity Payment using Present Value using this online evaluator? To use this online evaluator 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.

FAQs on Growing Annuity Payment using Present Value

What is the formula to find Growing Annuity Payment using Present Value?

The formula of Growing Annuity Payment using Present Value is expressed as Initial Payment = Present Value*((Rate per Period-Growth Rate)/(1-(((1+Growth Rate)/(1+Rate per Period))^Number of Periods))). Here is an example- 53.26087 = 100*((0.05-0.02)/(1-(((1+0.02)/(1+0.05))^2))).

How to calculate Growing Annuity Payment using Present Value?

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

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Growing Annuity Payment using Present Value Formula

Growing Annuity Payment using Present Value Example

Growing Annuity Payment using Present Value Solution

Growing Annuity Payment using Present Value Formula Elements

Other formulas in Present Value category

How to Evaluate Growing Annuity Payment using Present Value?

FAQs on Growing Annuity Payment using Present Value

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