## Number of Periods using Present Value of Annuity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Number of Periods = ln((1-(Present Value of Annuity/Cashflow per Period))^-1)/ln(1+Rate per Period)
t = ln((1-(PVAnnuity/Cf))^-1)/ln(1+r)
This formula uses 1 Functions, 4 Variables
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
Variables Used
Total Number of Periods - Total Number of Periods is the total number of compounding periods for the life of the investment.
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.
STEP 1: Convert Input(s) to Base Unit
Present Value of Annuity: 1460 --> No Conversion Required
Cashflow per Period: 1500 --> No Conversion Required
Rate per Period: 0.05 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
t = ln((1-(PVAnnuity/Cf))^-1)/ln(1+r) --> ln((1-(1460/1500))^-1)/ln(1+0.05)
Evaluating ... ...
t = 74.2842536948684
STEP 3: Convert Result to Output's Unit
74.2842536948684 --> No Conversion Required
FINAL ANSWER
74.2842536948684 74.28425 <-- Total Number of Periods
(Calculation completed in 00.004 seconds)
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Created by Keerthika Bathula
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
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
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
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
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
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
Present Value = Future Value/(1+(Rate of Return/Compounding Periods))^(Compounding Periods*Number of Periods)
Number of Periods using Present Value of Annuity
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
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
Present Value of Annuity = Cashflow per Period*((1-e^(-Rate per Period*Number of Periods))/(e^Rate per Period-1))
Present Value of Annuity
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
Present Value = Future Value/exp(Rate of Return*Number of Periods)
Present Value for Continuous Compounding
Present Value with Continuous Compounding = Future Value/(e^(Rate per Period*Number of Periods))
Present Value Factor
Annuity Present Value Factor = (1-((1+Rate per Period)^(-Number of Periods)))/Rate per Period
Present Value of Stock with Constant Growth
Price of Stock = Estimated Dividends for Next Period/((Rate of Return*0.01)-Growth Rate)
Present Value of Lumpsum
Present Value of Lumpsum = Future Value/(1+Interest Rate per Period)^Number of Periods
Present Value of Future Sum given Total Number of Periods
Present Value = Future Value/(1+Interest Rate)^Total Number of Periods
Present Value Continuous Compounding Factor
PV Continuous Compounding Factor = (e^(-Rate per Period*Total Number of Periods))
PV of Perpetuity
PV of Perpetuity = Dividend/Discount Rate
Present Value of Stock with Zero Growth
Price of Stock = Dividend/Rate of Return

## Number of Periods using Present Value of Annuity Formula

Total Number of Periods = ln((1-(Present Value of Annuity/Cashflow per Period))^-1)/ln(1+Rate per Period)
t = ln((1-(PVAnnuity/Cf))^-1)/ln(1+r)

## What is Number of Periods using Present Value of Annuity?

The number of periods using the present value of an annuity refers to the length of time it takes for a series of regular payments, made at a fixed interest rate, to accumulate to a specified present value. This concept is crucial in financial planning and investment analysis, as it helps determine the duration required to achieve a particular financial goal or pay off a debt. By knowing the present value, the annuity payment amount, and the interest rate, individuals and businesses can calculate the number of periods needed to reach their desired financial target. This calculation is essential in areas such as retirement planning, loan repayment schedules, and investment projections, providing a clear timeline for achieving financial objectives.

## How to Calculate Number of Periods using Present Value of Annuity?

Number of Periods using Present Value of Annuity calculator uses Total Number of Periods = ln((1-(Present Value of Annuity/Cashflow per Period))^-1)/ln(1+Rate per Period) to calculate the Total Number of Periods, The Number of Periods using Present Value of Annuity formula is defined as the time duration over which regular payments (PMT) at a certain interest rate (r) will accumulate to equal the desired present value (PV). Total Number of Periods is denoted by t symbol.

How to calculate Number of Periods using Present Value of Annuity using this online calculator? To use this online calculator for Number of Periods using Present Value of Annuity, enter Present Value of Annuity (PVAnnuity), Cashflow per Period (Cf) & Rate per Period (r) and hit the calculate button. Here is how the Number of Periods using Present Value of Annuity calculation can be explained with given input values -> 8.938725 = ln((1-(1460/1500))^-1)/ln(1+0.05).

### FAQ

What is Number of Periods using Present Value of Annuity?
The Number of Periods using Present Value of Annuity formula is defined as the time duration over which regular payments (PMT) at a certain interest rate (r) will accumulate to equal the desired present value (PV) and is represented as t = ln((1-(PVAnnuity/Cf))^-1)/ln(1+r) or Total Number of Periods = ln((1-(Present Value of Annuity/Cashflow per Period))^-1)/ln(1+Rate per Period). 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 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.
How to calculate Number of Periods using Present Value of Annuity?
The Number of Periods using Present Value of Annuity formula is defined as the time duration over which regular payments (PMT) at a certain interest rate (r) will accumulate to equal the desired present value (PV) is calculated using Total Number of Periods = ln((1-(Present Value of Annuity/Cashflow per Period))^-1)/ln(1+Rate per Period). To calculate Number of Periods using Present Value of Annuity, you need Present Value of Annuity (PVAnnuity), Cashflow per Period (Cf) & Rate per Period (r). With our tool, you need to enter the respective value for Present Value of Annuity, Cashflow per Period & Rate per Period 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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