Effective annual rate - Revision history

imported>Doug Williamson: Layout.

2023-03-29T11:51:35Z

Layout.

← Older revision		Revision as of 11:51, 29 March 2023
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	USD short term interest is conventionally quoted on a simple interest basis for a 360-day year.		USD short term interest is conventionally quoted on a simple interest basis for a 360-day year.

	Let's assume for this example the overnight interest rate quoted for USD is 5.11% (the same headline interest rate as in ~~example~~ 3, but for USD in this case).		Let's assume for this example the overnight interest rate quoted for USD is 5.11% (the same headline interest rate as in Example 3, but for USD in this case).

	USD overnight interest quoted at R = 5.11% means:		USD overnight interest quoted at R = 5.11% means:

imported>Doug Williamson: Expand explanation.

2023-03-28T07:38:43Z

Expand explanation.

← Older revision		Revision as of 07:38, 28 March 2023
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	n = number of times the period fits into a conventional year (for example, 360 or 365 days)		n = number of times the period fits into a conventional year (for example, 360 or 365 days)

			---

			Examples 3 and 4 illustrate the conversion from an interest rate quoted on a nominal annual basis, to an EAR.


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	GBP overnight interest is conventionally quoted on a simple interest basis for a 365-day fixed year.		GBP overnight interest is conventionally quoted on a simple interest basis for a 365-day fixed year.

	So GBP overnight interest quoted at R = 5.11% means:		Let's assume for this example that the overnight interest rate quoted for GBP is 5.11%.

			GBP overnight interest quoted at R = 5.11% means:

	(i)		(i)
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	USD short term interest is conventionally quoted on a simple interest basis for a 360-day year.		USD short term interest is conventionally quoted on a simple interest basis for a 360-day year.

	So USD overnight interest quoted at R = 5.11% means:		Let's assume for this example the overnight interest rate quoted for USD is 5.11% (the same headline interest rate as in example 3, but for USD in this case).

			USD overnight interest quoted at R = 5.11% means:

	(i)		(i)
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	EAR = '''5.3171%'''.		EAR = '''5.3171%'''.

			(This is greater than the EAR calculated for GBP in Example 3, because short term USD uses a 360-day conventional year, compared with 365 days for GBP.)


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	* [[Continuously compounded rate of return]]		* [[Continuously compounded rate of return]]
	* [[Effective annual yield]]		* [[Effective annual yield]]
			* [[Headline ]]
	* [[Leap year]]		* [[Leap year]]
	* [[LIBOR]]		* [[LIBOR]]

imported>Doug Williamson: Remove surplus link.

2022-06-25T10:27:12Z

Remove surplus link.

← Older revision		Revision as of 10:27, 25 June 2022
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	== See also ==		== See also ==
	* [[AER]]
	* [[ACT/365 fixed]]		* [[ACT/365 fixed]]
	* [[Annual effective rate]] (AER)		* [[Annual effective rate]] (AER)

imported>Doug Williamson: Remove surplus link.

2022-03-12T20:56:07Z

Remove surplus link.

← Older revision		Revision as of 20:56, 12 March 2022
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	* [[Continuously compounded rate of return]]		* [[Continuously compounded rate of return]]
	* [[Effective annual yield]]		* [[Effective annual yield]]
	* [[Equivalent Annual Rate]]
	* [[Leap year]]		* [[Leap year]]
	* [[LIBOR]]		* [[LIBOR]]

imported>Doug Williamson: Update links.

2022-03-12T20:55:33Z

Update links.

← Older revision		Revision as of 20:55, 12 March 2022
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	* [[AER]]		* [[AER]]
	* [[ACT/365 fixed]]		* [[ACT/365 fixed]]
	* [[Annual effective rate]]		* [[Annual effective rate]] (AER)
	* [[Annual effective yield]]		* [[Annual effective yield]]
	* [[Annual percentage rate]]		* [[Annual percentage rate]] (APR)
	* [[Basis]]		* [[Basis]]
	* [[Benchmark]]		* [[Benchmark]]

imported>Doug Williamson: Add link.

2022-03-09T22:04:09Z

Add link.

← Older revision		Revision as of 22:04, 9 March 2022
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	* [[Annual effective yield]]		* [[Annual effective yield]]
	* [[Annual percentage rate]]		* [[Annual percentage rate]]
			* [[Basis]]
	* [[Benchmark]]		* [[Benchmark]]
	* [[Calculating effective annual rates]]		* [[Calculating effective annual rates]]

imported>Doug Williamson: Layout.

2022-03-05T08:59:19Z

Layout.

← Older revision		Revision as of 08:59, 5 March 2022
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	~~==Calculating EAR from overnight nominal annual quotes==~~		<span style="color:#4B0082">'''Example 3: EAR from overnight quote (R)'''</span>

	<span style="color:#4B0082">'''Example 3: EAR from overnight quote'''</span>

	GBP overnight interest is conventionally quoted on a simple interest basis for a 365-day fixed year.		GBP overnight interest is conventionally quoted on a simple interest basis for a 365-day fixed year.

imported>Doug Williamson: Layout.

2022-03-05T08:58:08Z

Layout.

← Older revision		Revision as of 08:58, 5 March 2022
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	<span style="color:#4B0082">'''''~~Conversion~~ from other rates to Effective annual rate'''''</span>		<span style="color:#4B0082">'''''CONVERSION from other rates to Effective annual rate'''''</span>


	<span style="color:#4B0082">'''''(i) Converting periodic interest rate or yield (r) to Effective annual rate (EAR)'''''</span>		<span style="color:#4B0082">'''''(i) Converting periodic interest rate or yield (r) to Effective annual rate (EAR)'''''</span>

imported>Doug Williamson: Layout.

2022-03-05T08:57:08Z

Layout.

← Older revision		Revision as of 08:57, 5 March 2022
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			<span style="color:#4B0082">'''''Conversion from other rates to Effective annual rate'''''</span>

	=~~=Conversion formulae==~~		<span style="color:#4B0082">'''''(i) Converting periodic interest rate or yield (r) to Effective annual rate (EAR)'''''</span>

			''EAR = (1 + r)<sup>n</sup> - 1''
	~~====Converting periodic interest rate or yield to Effective annual rate====~~

	EAR = (1 + r)<sup>n</sup> - 1


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	=~~===~~Converting nominal annual rate to periodic rate~~====~~		<span style="color:#4B0082">'''''(ii) Converting nominal annual rate (R) to periodic rate (r)'''''</span>

	r = R / n		''r = R / n''

imported>Doug Williamson: Add simple interest calculations.

2022-03-04T21:15:02Z

Add simple interest calculations.

← Older revision		Revision as of 21:15, 4 March 2022
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	(EAR).		(EAR).
	__NOTOC__		__NOTOC__

	1.		1.

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	EAR = '''67.8%'''.		EAR = '''67.8%'''.


			Out of this total, the amount relating to interest on the original principal - simple interest - is 52 weeks x 1% per week = 52%.

			The rest of the total of 67.8% is the additional amount due to compounding - interest on interest.


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	EAR = '''12.68%'''.		EAR = '''12.68%'''.


			Out of this total, the amount relating to interest on the original principal - simple interest - is 12 months x 1% per month = 12%.

			The rest of the total of 12.68% is the additional amount due to compounding - interest on interest.


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	* [[Certificate in Treasury]]		* [[Certificate in Treasury]]
	* [[Compound]]		* [[Compound]]
			* [[Compound interest]]
	* [[Continuously compounded rate of return]]		* [[Continuously compounded rate of return]]
	* [[Effective annual yield]]		* [[Effective annual yield]]
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	* [[Risk]]		* [[Risk]]
	* [[Semi-annual rate]]		* [[Semi-annual rate]]
			* [[Simple interest]]

	[[Category:Long_term_funding]]		[[Category:Long_term_funding]]
	[[Category:Cash_management]]		[[Category:Cash_management]]