Macaulay Duration Calculator

✖Cash Flow Number refers to the serial wise number of cash flow which is to be used while adding.ⓘ Cash Flow Number [cfn]			+10% -10%
✖Cash Flow, in general, refers to payments made into or out of a business, project, or financial product.ⓘ Cash Flow [CF]			+10% -10%
✖Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until the end of its lifetime.ⓘ Yield to Maturity (YTM) [YTM]			+10% -10%
✖Compounding Periods is the number of times compounding will occur during a period.ⓘ Compounding Periods [n_c]			+10% -10%
✖Time in Years refers to a duration or period measured in terms of the number of years elapsed or anticipated.ⓘ Time in Years [T_yrs]			+10% -10%
✖The present value of the annuity is the value that determines the value of a series of future periodic payments at a given time.ⓘ Present Value [PV]			+10% -10%

✖Macaulay Duration is the weighted average time until cash flows are received.ⓘ Macaulay Duration [Macaulay_dur]

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Formula

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Macaulay Duration

Formula

`"Macaulay"_{"dur"} = sum(x,1,5,"cfn",(("CF"/(1+"YTM"/"n"_{"c"}))^"cfn"))*("T"_{"yrs"}/"PV")`

Example

`"2"=sum(x,1,5,"5",(("1050"/(1+"12"/"10"))^"5"))*("4"/"10")`

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Macaulay Duration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Macaulay Duration = sum(x,1,5,Cash Flow Number,((Cash Flow/(1+Yield to Maturity (YTM)/Compounding Periods))^Cash Flow Number))*(Time in Years/Present Value)
Macaulay_dur = sum(x,1,5,cfn,((CF/(1+YTM/n_c))^cfn))*(T_yrs/PV)
This formula uses 1 Functions, 7 Variables

Functions Used

sum - Summation or sigma (∑) notation is a method used to write out a long sum in a concise way., sum(i, from, to, expr)

Variables Used

Macaulay Duration - Macaulay Duration is the weighted average time until cash flows are received.
Cash Flow Number - Cash Flow Number refers to the serial wise number of cash flow which is to be used while adding.
Cash Flow - Cash Flow, in general, refers to payments made into or out of a business, project, or financial product.
Yield to Maturity (YTM) - Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until the end of its lifetime.
Compounding Periods - Compounding Periods is the number of times compounding will occur during a period.
Time in Years - Time in Years refers to a duration or period measured in terms of the number of years elapsed or anticipated.
Present Value - The present value of the annuity is the value that determines the value of a series of future periodic payments at a given time.

STEP 1: Convert Input(s) to Base Unit

Cash Flow Number: 5 --> No Conversion Required
Cash Flow: 1050 --> No Conversion Required
Yield to Maturity (YTM): 12 --> No Conversion Required
Compounding Periods: 10 --> No Conversion Required
Time in Years: 4 --> No Conversion Required
Present Value: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Macaulay_dur = sum(x,1,5,cfn,((CF/(1+YTM/n_c))^cfn))*(T_yrs/PV) --> sum(x,1,5,5,((1050/(1+12/10))^5))*(4/10)

Evaluating ... ...

Macaulay_dur = 2

STEP 3: Convert Result to Output's Unit

2 --> No Conversion Required

FINAL ANSWER

2 <-- Macaulay Duration

(Calculation completed in 00.004 seconds)

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Created by Kashish Arora

Satyawati College (DU), New Delhi

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< 4 Business Calculators

Macaulay Duration

Go Macaulay Duration = sum(x,1,5,Cash Flow Number,((Cash Flow/(1+Yield to Maturity (YTM)/Compounding Periods))^Cash Flow Number))*(Time in Years/Present Value)

Inventory Shrinkage

Go Inventory Shrinkage = ((Recorded Inventory-Actual Inventory)/Recorded Inventory)*100

Modified Duration

Go Modified Duration = Macaulay Duration/(1+Yield to Maturity (YTM)/Coupon Periods)

Retention Ratio

Go Retention Ratio = (Net Income-Dividend)/Net Income

Macaulay Duration Formula

What is Macaulay Duration?

Macaulay duration finds the present value of a bond’s future coupon payments and maturity value. Fortunately for investors, this measure is a standard data point in most bond searching and analysis software tools. Because Macaulay duration is a partial function of the time to maturity, the greater the duration, the greater the interest rate risk or reward for bond prices.

How to Calculate Macaulay Duration?

Macaulay Duration calculator uses Macaulay Duration = sum(x,1,5,Cash Flow Number,((Cash Flow/(1+Yield to Maturity (YTM)/Compounding Periods))^Cash Flow Number))*(Time in Years/Present Value) to calculate the Macaulay Duration, The Macaulay Duration formula helps to find the present value of a bond’s future coupon payments and maturity value. Macaulay Duration is denoted by Macaulay_dur symbol.

How to calculate Macaulay Duration using this online calculator? To use this online calculator for Macaulay Duration, enter Cash Flow Number (cfn), Cash Flow (CF), Yield to Maturity (YTM) (YTM), Compounding Periods (n_c), Time in Years (T_yrs) & Present Value (PV) and hit the calculate button. Here is how the Macaulay Duration calculation can be explained with given input values -> 2 = sum(x,1,5,5,((1050/(1+12/10))^5))*(4/10).

FAQ

What is Macaulay Duration?

The Macaulay Duration formula helps to find the present value of a bond’s future coupon payments and maturity value and is represented as Macaulay_dur = sum(x,1,5,cfn,((CF/(1+YTM/n_c))^cfn))*(T_yrs/PV) or Macaulay Duration = sum(x,1,5,Cash Flow Number,((Cash Flow/(1+Yield to Maturity (YTM)/Compounding Periods))^Cash Flow Number))*(Time in Years/Present Value). Cash Flow Number refers to the serial wise number of cash flow which is to be used while adding, Cash Flow, in general, refers to payments made into or out of a business, project, or financial product, Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until the end of its lifetime, Compounding Periods is the number of times compounding will occur during a period, Time in Years refers to a duration or period measured in terms of the number of years elapsed or anticipated & The present value of the annuity is the value that determines the value of a series of future periodic payments at a given time.

How to calculate Macaulay Duration?

The Macaulay Duration formula helps to find the present value of a bond’s future coupon payments and maturity value is calculated using Macaulay Duration = sum(x,1,5,Cash Flow Number,((Cash Flow/(1+Yield to Maturity (YTM)/Compounding Periods))^Cash Flow Number))*(Time in Years/Present Value). To calculate Macaulay Duration, you need Cash Flow Number (cfn), Cash Flow (CF), Yield to Maturity (YTM) (YTM), Compounding Periods (n_c), Time in Years (T_yrs) & Present Value (PV). With our tool, you need to enter the respective value for Cash Flow Number, Cash Flow, Yield to Maturity (YTM), Compounding Periods, Time in Years & Present Value 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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