Present Value of Annuity with Continuous Compounding Solution

STEP 0: Pre-Calculation Summary
Formula Used
Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1))
PVAnnuity = Cf*((1-e^(-r*nPeriods))/(e^r-1))
This formula uses 1 Constants, 4 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Variables Used
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.
Cashflow per Period - Cashflow per Period refers to the amount of money that is either received or paid out at regular intervals.
Rate per Period - The Rate per Period is the interest rate charged.
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
Cashflow per Period: 1500 --> No Conversion Required
Rate per Period: 0.05 --> No Conversion Required
Number of Periods: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PVAnnuity = Cf*((1-e^(-r*nPeriods))/(e^r-1)) --> 1500*((1-e^(-0.05*2))/(e^0.05-1))
Evaluating ... ...
PVAnnuity = 2784.10026380501
STEP 3: Convert Result to Output's Unit
2784.10026380501 --> No Conversion Required
FINAL ANSWER
2784.10026380501 2784.1 <-- Present Value of Annuity
(Calculation completed in 00.004 seconds)

Credits

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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

Present Value of Annuity with Continuous Compounding Formula

Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1))
PVAnnuity = Cf*((1-e^(-r*nPeriods))/(e^r-1))

What is Present Value of Annuity with Continuous Compounding ?

The present value (PV) of an annuity with continuous compounding is a fundamental financial concept used to determine 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. Unlike traditional compounding methods that compound interest at discrete intervals, continuous compounding assumes that interest is added to the principal balance infinitely often, resulting in a more precise calculation of the annuity's present value. This concept is essential in finance for evaluating the current value of future cash flows, aiding in investment decision-making, loan calculations, and financial planning strategies.




How to Calculate Present Value of Annuity with Continuous Compounding?

Present Value of Annuity with Continuous Compounding calculator uses Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1)) to calculate 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 calculate Present Value of Annuity with Continuous Compounding using this online calculator? To use this online calculator for Present Value of Annuity with Continuous Compounding, enter Cashflow per Period (Cf), Rate per Period (r) & Number of Periods (nPeriods) and hit the calculate button. Here is how the Present Value of Annuity with Continuous Compounding calculation can be explained with given input values -> 1461.615 = 1500*((1-e^(-0.05*2))/(e^0.05-1)).

FAQ

What is Present Value of Annuity with Continuous Compounding?
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 and is represented as PVAnnuity = Cf*((1-e^(-r*nPeriods))/(e^r-1)) or Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1)). Cashflow per Period refers to the amount of money that is either received or paid out at regular intervals, The Rate per Period is the interest rate charged & 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 Annuity with Continuous Compounding?
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 is calculated using Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1)). To calculate Present Value of Annuity with Continuous Compounding, you need Cashflow per Period (Cf), Rate per Period (r) & Number of Periods (nPeriods). With our tool, you need to enter the respective value for Cashflow per Period, Rate per Period & Number of Periods and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Present Value of Annuity?
In this formula, Present Value of Annuity uses Cashflow per Period, Rate per Period & Number of Periods. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Present Value of Annuity = (Monthly Payment/Interest Rate)*(1-(1/(1+Interest Rate)^Number of Months))
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