imported>Doug Williamson: Classify page.

2022-06-27T18:00:05Z

Classify page.

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	* [[Semi-annual rate]]		* [[Semi-annual rate]]
	*[[SONIA]]		*[[SONIA]]

			[[Category:The_business_context]]

imported>Doug Williamson: Update links.

2022-04-26T09:57:28Z

Update links.

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	* [[Effective annual yield]]		* [[Effective annual yield]]
	* [[Equivalent Annual Rate]]		* [[Equivalent Annual Rate]]
	* [[LIBOR]]
	* [[Nominal annual rate]]		* [[Nominal annual rate]]
	* [[Periodic discount rate]]		* [[Periodic discount rate]]
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			*[[SONIA]]

imported>Doug Williamson: Create the page. Source: Effective annual rate page.

2015-12-03T17:46:23Z

Create the page. Source: Effective annual rate page.

New page

Effective annual rate (EAR) is a conventional measure which expresses the returns on different instruments on a comparable basis.

The EAR basis of comparison is the ''equivalent'' rate of interest paid and compounded annually, which would give the same all-in rate of return as the instrument under review.

For this reason, 'EAR' is sometimes expressed as equivalent annual rate.

==Conversion formulae==

====Nominal annual rate to periodic rate====

r = R / n

''Where:''

r = periodic interest rate or yield

R = nominal annual rate

n = number of times the period fits into a conventional year (for example, 360 or 365 days)

====Periodic interest rate or yield to Effective annual rate====

EAR = (1 + r)n - 1

''Where:''

EAR = effective annual rate or yield

r = periodic interest rate or yield, as before

n = number of times the period fits into a calendar year

==EAR from semi-annual quote==

We can calculate EAR from a semi-annual (half-year) quote.

'''Example 1: EAR from semi-annual quote'''

GBP semi-annual interest is conventionally quoted on a simple interest basis for half-years, using half-years to calculate interest for each period of six months, rather than an exact daycount.

So GBP semi-annual interest quoted at R = 5.00% means:

(i)

Interest of:

r = R / n

r = 5.00 / 2

r = 2.50% is paid per six months.

(ii)

The ''equivalent'' effective annual rate is:

EAR = (1 + r)n - 1

EAR = 1.0252 - 1

EAR = '''5.0625%'''.

==EAR from USD overnight quote==

We can calculate EAR from a USD overnight quote which has a 360-day year.

'''Example 2: EAR from USD overnight quote'''

USD overnight interest is conventionally quoted on a simple interest basis for a 360-day year.

So USD overnight interest quoted at R = 5.04% means:

(i)

Interest of:

r = R / n

r = 5.04% / 360

r = 0.014% is paid per day.

(ii)

The ''equivalent'' effective annual rate is:

EAR = (1 + r)n - 1

EAR = 1.00014365 - 1

EAR = '''5.2424%'''.

== See also ==
* [[ACT/365 fixed]]
* [[Annual effective rate]]
* [[Annual effective yield]]
* [[Annual percentage rate]]
* [[Capital market]]
* [[Certificate in Treasury Fundamentals]]
* [[Certificate in Treasury]]
* [[Continuously compounded rate of return]]
* [[Effective annual rate]]
* [[Effective annual yield]]
* [[Equivalent Annual Rate]]
* [[LIBOR]]
* [[Nominal annual rate]]
* [[Periodic discount rate]]
* [[Periodic rate of interest]]
* [[Periodic yield]]
* [[Rate of return]]
* [[Real]]
* [[Return]]
* [[Semi-annual rate]]

Calculating effective annual rates - Revision history

imported>Doug Williamson: Classify page.

imported>Doug Williamson: Update links.

imported>Doug Williamson: Create the page. Source: Effective annual rate page.