Number of Periods using Present Value of Annuity Calculator

✖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.ⓘ Present Value of Annuity [PVAnnuity]			+10% -10%
✖Cashflow per Period refers to the amount of money that is either received or paid out at regular intervals.ⓘ Cashflow per Period [C_f]			+10% -10%
✖The Rate per Period is the interest rate charged.ⓘ Rate per Period [r]			+10% -10%

✖Total Number of Periods is the total number of compounding periods for the life of the investment.ⓘ Number of Periods using Present Value of Annuity [t]

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Formula

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Number of Periods using Present Value of Annuity

Formula

`"t" = ln((1-("PVAnnuity"/"C"_{"f"}))^-1)/ln(1+"r")`

Example

`"74.28425"=ln((1-("1460"/"1500"))^-1)/ln(1+"0.05")`

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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/C_f))^-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/C_f))^-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

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

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/C_f))^-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 (C_f) & 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/C_f))^-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 (C_f) & 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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