Future Value of Annuity with Continuous Compounding Solution

STEP 0: Pre-Calculation Summary
Formula Used
FV of Annuity with Continuous Compounding = Cashflow per Period*((e^(Rate per Period*Number of Periods)-1)/(e^(Rate per Period)-1))
FVACC = Cf*((e^(r*nPeriods)-1)/(e^(r)-1))
This formula uses 1 Constants, 4 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Variables Used
FV of Annuity with Continuous Compounding - FV of Annuity with Continuous Compounding refers to the total value accrued from regular payments compounded continuously over a specified time period.
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
FVACC = Cf*((e^(r*nPeriods)-1)/(e^(r)-1)) --> 1500*((e^(0.05*2)-1)/(e^(0.05)-1))
Evaluating ... ...
FVACC = 3076.90664456403
STEP 3: Convert Result to Output's Unit
3076.90664456403 --> No Conversion Required
FINAL ANSWER
3076.90664456403 3076.907 <-- FV of Annuity with Continuous Compounding
(Calculation completed in 00.004 seconds)

Credits

Created by Keerthika Bathula
Indian Institute of Technology, Indian School of mines, Dhanbad (IIT ISM Dhanbad), Dhanbad
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BMS College of Engineering (BMSCE), Bangalore
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14 Future value Calculators

Future Value of Growing Annuity
Go Future Value of Growing Annuity = Initial Investment*((1+Rate per Period)^(Number of Periods)-(1+Growth Rate)^(Number of Periods))/(Rate per Period-Growth Rate)
Growing Annuity Payment using Future Value
Go Initial Payment = (Future Value*(Rate per Period-Growth Rate))/(((1+Rate per Period)^(Number of Periods))-((1+Growth Rate)^(Number of Periods)))
Number of Periods using Future Value
Go Number of Periods = ln(1+((Future Value of Annuity*Rate per Period)/Cashflow per Period))/ln(1+Rate per Period)
Annuity Due for Future Value
Go Annuity Due Future Value = Payment made in Each Period*((1+Rate per Period)^(Number of Periods)-1)/(Rate per Period)*(1+Rate per Period)
Future Value of Present Sum given Compounding Periods
Go Future Value = Present Value*(1+((Rate of Return*0.01)/Compounding Periods))^(Compounding Periods*Number of Periods)
Future Value of Annuity with Continuous Compounding
Go FV of Annuity with Continuous Compounding = Cashflow per Period*((e^(Rate per Period*Number of Periods)-1)/(e^(Rate per Period)-1))
Future Value of Ordinary Annuities and Sinking Funds
Go Future Value of Ordinary Annuity = Cashflow per Period*((1+Rate per Period)^(Total Number of Times Compounded)-1)/Rate per Period
Future Value of Annuity
Go Future Value of Annuity = (Monthly Payment/(Interest Rate*0.01))*((1+(Interest Rate*0.01))^Number of Periods-1)
Future Value with Continuous Compounding
Go Future Value with Continuous Compounding = Present Value*(e^(Rate of Return*Number of Compounding Periods*0.01))
Future Value of Present Sum given Number of Periods
Go Future Value = Present Value*exp(Rate of Return*Number of Periods*0.01)
Future Value of Lumpsum
Go Future Value of Lumpsum = Present Value*(1+Interest Rate per Period)^Number of Periods
Annuity Payment using Future Value
Go Annuity Payment = Future Value of Annuity/(((1+Rate per Period)^Number of Periods)-1)
Future Value of Present Sum given Total Number of Periods
Go Future Value = Present Value*(1+(Rate of Return*0.01))^Number of Periods
Future Value Factor
Go Future Value Factor = (1+Rate per Period)^Number of Periods

Future Value of Annuity with Continuous Compounding Formula

FV of Annuity with Continuous Compounding = Cashflow per Period*((e^(Rate per Period*Number of Periods)-1)/(e^(Rate per Period)-1))
FVACC = Cf*((e^(r*nPeriods)-1)/(e^(r)-1))

What is Future Value of Annuity with Continuous Compounding?

The future value (FV) of an annuity with continuous compounding is a concept in finance that helps determine the total 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, which compounds interest at discrete intervals (such as annually, quarterly, or monthly), continuous compounding assumes that interest is added to the principal balance infinitely often, resulting in a higher overall value over time.This concept is particularly relevant in investment scenarios where interest is compounded continuously, such as in certain types of bonds or investment products that offer continuous growth potential.

How to Calculate Future Value of Annuity with Continuous Compounding?

Future Value of Annuity with Continuous Compounding calculator uses FV of Annuity with Continuous Compounding = Cashflow per Period*((e^(Rate per Period*Number of Periods)-1)/(e^(Rate per Period)-1)) to calculate the FV of Annuity with Continuous Compounding, The Future Value of Annuity with Continuous Compounding represents the total value of regular payments compounded continuously over a specific period at a given interest rate. FV of Annuity with Continuous Compounding is denoted by FVACC symbol.

How to calculate Future Value of Annuity with Continuous Compounding using this online calculator? To use this online calculator for Future 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 Future Value of Annuity with Continuous Compounding calculation can be explained with given input values -> 3076.907 = 1500*((e^(0.05*2)-1)/(e^(0.05)-1)).

FAQ

What is Future Value of Annuity with Continuous Compounding?
The Future Value of Annuity with Continuous Compounding represents the total value of regular payments compounded continuously over a specific period at a given interest rate and is represented as FVACC = Cf*((e^(r*nPeriods)-1)/(e^(r)-1)) or FV of Annuity with Continuous Compounding = Cashflow per Period*((e^(Rate per Period*Number of Periods)-1)/(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 Future Value of Annuity with Continuous Compounding?
The Future Value of Annuity with Continuous Compounding represents the total value of regular payments compounded continuously over a specific period at a given interest rate is calculated using FV of Annuity with Continuous Compounding = Cashflow per Period*((e^(Rate per Period*Number of Periods)-1)/(e^(Rate per Period)-1)). To calculate Future 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.
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