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Present Value of Annuity with Continuous Compounding Formula

GoPresent Value of Annuity Formula

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Present Value of Annuity is the current value of a set of cash flows in the future, given a specified rate of return or discount rate. Check FAQs

PVAnnuity = C f \cdot (\frac{1 - e^{- r \cdot n Periods}}{e^{r} - 1})

PVAnnuity - Present Value of Annuity?C_f - Cashflow per Period?r - Rate per Period?n_Periods - Number of Periods?

Present Value of Annuity with Continuous Compounding Example

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

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

Here is how the Present Value of Annuity with Continuous Compounding equation looks like.

2784.1003 = 1500 \cdot (\frac{1 - e^{- 0.05 \cdot 2}}{e^{0.05} - 1})

2784.1003 = 1500 \cdot (\frac{1 - e^{- 0.05 \cdot 2}}{e^{0.05} - 1})

2784.1003 = 1500 \cdot (\frac{1 - e^{- 0.05 \cdot 2}}{e^{0.05} - 1})

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Present Value » fx Present Value of Annuity with Continuous Compounding

Present Value of Annuity with Continuous Compounding Solution

Follow our step by step solution on how to calculate Present Value of Annuity with Continuous Compounding?

FIRST Step Consider the formula

PVAnnuity = C f \cdot (\frac{1 - e^{- r \cdot n Periods}}{e^{r} - 1})

Next Step Substitute values of Variables

∴

PVAnnuity = 1500 \cdot (\frac{1 - e^{- 0.05 \cdot 2}}{e^{0.05} - 1})

Next Step Prepare to Evaluate

∴

PVAnnuity = 1500 \cdot (\frac{1 - e^{- 0.05 \cdot 2}}{e^{0.05} - 1})

Next Step Evaluate

∴

PVAnnuity = 2784.10026380501

LAST Step Rounding Answer

∴

PVAnnuity = 2784.1003

Present Value of Annuity with Continuous Compounding Formula Elements

Variables

Present Value of Annuity

Present Value of Annuity is the current value of a set of cash flows in the future, given a specified rate of return or discount rate.

Symbol: PVAnnuity

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Present Value of Annuity

Cashflow per Period

Cashflow per Period refers to the amount of money that is either received or paid out at regular intervals.

Symbol: C_f

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cashflow per Period

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

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 to find Present Value of Annuity

Go Present Value of Annuity

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

Other formulas in Present Value category

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)}

Go Present Value of Lumpsum

PV L = \frac{FV}{{(1 + IR P)}^{n Periods}}

How to Evaluate Present Value of Annuity with Continuous Compounding?

Present Value of Annuity with Continuous Compounding evaluator uses Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1)) to evaluate the Present Value of Annuity, The Present Value of Annuity with Continuous Compounding represents the current worth of a series of regular payments made at equal intervals and compounded continuously over a specific period at a given interest rate. Present Value of Annuity is denoted by PVAnnuity symbol.

How to evaluate Present Value of Annuity with Continuous Compounding using this online evaluator? To use this online evaluator for Present Value of Annuity with Continuous Compounding, enter Cashflow per Period (C_f), Rate per Period (r) & Number of Periods (n_Periods) and hit the calculate button.

FAQs on Present Value of Annuity with Continuous Compounding

What is the formula to find Present Value of Annuity with Continuous Compounding?

The formula of Present Value of Annuity with Continuous Compounding is expressed as Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1)). Here is an example- 1461.615 = 1500*((1-e^(-0.05*2))/(e^0.05-1)).

How to calculate Present Value of Annuity with Continuous Compounding?

With Cashflow per Period (C_f), Rate per Period (r) & Number of Periods (n_Periods) we can find Present Value of Annuity with Continuous Compounding using the formula - Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1)).

What are the other ways to Calculate Present Value of Annuity?

Here are the different ways to Calculate Present Value of Annuity-

Present Value of Annuity=(Monthly Payment/Interest Rate)*(1-(1/(1+Interest Rate)^Number of Months))

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Present Value of Annuity with Continuous Compounding Formula

​GoPresent Value of Annuity Formula

Present Value of Annuity with Continuous Compounding Example

Present Value of Annuity with Continuous Compounding Solution

Present Value of Annuity with Continuous Compounding Formula Elements

Other Formulas to find Present Value of Annuity

Other formulas in Present Value category

How to Evaluate Present Value of Annuity with Continuous Compounding?

FAQs on Present Value of Annuity with Continuous Compounding

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GoPresent Value of Annuity Formula