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Macaulay Duration Formula

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Macaulay Duration is the weighted average time until cash flows are received. Check FAQs

Macaulay dur = \sum (x, 1, 5, cfn, ({(\frac{CF}{1 + \frac{YTM}{n c}})}^{cfn})) \cdot (\frac{T yrs}{PV})

Macaulay_dur - Macaulay Duration?cfn - Cash Flow Number?CF - Cash Flow?YTM - Yield to Maturity (YTM)?n_c - Compounding Periods?T_yrs - Time in Years?PV - Present Value?

Macaulay Duration Example

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Here is how the Macaulay Duration equation looks like with Values.

Here is how the Macaulay Duration equation looks like with Units.

Here is how the Macaulay Duration equation looks like.

2 = \sum (x, 1, 5, 5, ({(\frac{1050}{1 + \frac{12}{10}})}^{5})) \cdot (\frac{4}{10})

2 = \sum (x, 1, 5, 5, ({(\frac{1050}{1 + \frac{12}{10}})}^{5})) \cdot (\frac{4}{10})

2 = \sum (x, 1, 5, 5, ({(\frac{1050}{1 + \frac{12}{10}})}^{5})) \cdot (\frac{4}{10})

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Macaulay Duration Solution

Follow our step by step solution on how to calculate Macaulay Duration?

FIRST Step Consider the formula

Macaulay dur = \sum (x, 1, 5, cfn, ({(\frac{CF}{1 + \frac{YTM}{n c}})}^{cfn})) \cdot (\frac{T yrs}{PV})

Next Step Substitute values of Variables

∴

Macaulay dur = \sum (x, 1, 5, 5, ({(\frac{1050}{1 + \frac{12}{10}})}^{5})) \cdot (\frac{4}{10})

Next Step Prepare to Evaluate

∴

Macaulay dur = \sum (x, 1, 5, 5, ({(\frac{1050}{1 + \frac{12}{10}})}^{5})) \cdot (\frac{4}{10})

LAST Step Evaluate

∴

Macaulay dur = 2

Macaulay Duration Formula Elements

Variables

Functions

Macaulay Duration

Macaulay Duration is the weighted average time until cash flows are received.

Symbol: Macaulay_dur

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Macaulay Duration

Cash Flow Number

Cash Flow Number refers to the serial wise number of cash flow which is to be used while adding.

Symbol: cfn

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cash Flow Number

Cash Flow

Cash Flow, in general, refers to payments made into or out of a business, project, or financial product.

Symbol: CF

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cash Flow

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.

Symbol: YTM

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Yield to Maturity (YTM)

Compounding Periods

Compounding Periods is the number of times compounding will occur during a period.

Symbol: n_c

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Compounding Periods

Time in Years

Time in Years refers to a duration or period measured in terms of the number of years elapsed or anticipated.

Symbol: T_yrs

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Time in Years

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.

Symbol: PV

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Present Value

sum

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

Syntax: sum(i, from, to, expr)

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How to Evaluate Macaulay Duration?

Macaulay Duration evaluator 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 evaluate 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 evaluate Macaulay Duration using this online evaluator? To use this online evaluator 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.

FAQs on Macaulay Duration

What is the formula to find Macaulay Duration?

The formula of Macaulay Duration is expressed as 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). Here is an example- 2 = sum(x,1,5,5,((1050/(1+12/10))^5))*(4/10).

How to calculate Macaulay Duration?

With Cash Flow Number (cfn), Cash Flow (CF), Yield to Maturity (YTM) (YTM), Compounding Periods (n_c), Time in Years (T_yrs) & Present Value (PV) we can find Macaulay Duration using the formula - 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). This formula also uses Summation Notation (sum) function(s).

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Macaulay Duration Formula

Macaulay Duration Example

Macaulay Duration Solution

Macaulay Duration Formula Elements

Other formulas in Business category

How to Evaluate Macaulay Duration?

FAQs on Macaulay Duration

Variable Name