imported>Doug Williamson |
imported>Doug Williamson |
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| (EAR).
| | ''Governance - UK.'' |
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| | (EOA). |
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| A quoting convention under which interest at the quoted rate is calculated and added to the principal annually.
| | The Employee Ownership Association represents UK organisations which are employee owned, or transitioning to employee ownership. |
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| EAR is the most usual conventional quotation basis for instruments with maturities of greater than one year.
| | The EOA is a not-for-profit organisation that works to promote - and provide insight into - the business case for employee ownership. |
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| | ==See also== |
| | *[[Governance]] |
| | *[[Mutual]] |
| | *[[Not-for-profit]] |
| | *[[Shareholder]] |
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| A conventional measure which expresses the returns on different instruments on a comparable basis.
| | [[Category:Accounting,_tax_and_regulation]] |
| | | [[Category:The_business_context]] |
| 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.
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| For this reason, 'EAR' is sometimes expressed as <u>equivalent</u> annual rate.
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| ==Conversion formulae==
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| r = R / n
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| ''Where:''
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| r = periodic interest rate or yield
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| R = nominal annual rate
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| n = number of times the period fits into a conventional year (for example, 360 or 365 days)
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| EAR = (1 + r)<sup>n</sup> - 1
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| ''Where:''
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| EAR = effective annual rate or yield
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| r = periodic interest rate or yield, as before
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| n = number of times the period fits into a calendar year
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| ==Calculating EAR from GBP overnight quote==
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| <span style="color:#4B0082">'''Example 1: EAR from overnight quote'''</span>
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| GBP overnight interest is conventionally quoted on a simple interest basis for a 365-day year.
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| So GBP overnight interest quoted at R = 5.11% means:
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| Interest of:
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| r = R / n
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| r = 5.11% / 365
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| r = 0.014% (= 0.00014) is paid per day.
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| (ii)
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| The ''equivalent'' effective annual rate is calculated from (1 + r).
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| 1 + r = 1 + 0.00014 = 1.00014
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| EAR = (1 + r)<sup>n</sup> - 1
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| EAR = 1.00014<sup>365</sup> - 1
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| EAR = '''5.2424%'''.
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| ==EAR from semi-annual quote==
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| We can calculate EAR from a semi-annual (half-year) quote.
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| <span style="color:#4B0082">'''Example 2: EAR from semi-annual quote'''</span>
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| 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.
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| So GBP semi-annual interest quoted at R = 5.00% means:
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| (i)
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| Interest of:
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| r = R / n
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| r = 5.00 / 2
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| r = 2.50% is paid per six months.
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| (ii)
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| The ''equivalent'' effective annual rate is:
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| EAR = (1 + r)<sup>n</sup> - 1
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| EAR = 1.025<sup>2</sup> - 1
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| EAR = '''5.0625%'''.
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| ==EAR from USD overnight quote==
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| We can calculate EAR using USD overnight quote which has a 360-day year.
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| <span style="color:#4B0082">'''Example 3: EAR from USD overnight quote'''</span>
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| USD overnight interest is conventionally quoted on a simple interest basis for a 360-day year.
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| So USD overnight interest quoted at R = 5.04% means:
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| (i)
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| Interest of:
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| r = R / n
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| r = 5.04% / 360
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| r = 0.014% is paid per day.
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| (ii)
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| The ''equivalent'' effective annual rate is:
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| EAR = (1 + r)<sup>n</sup> - 1
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| EAR = 1.00014<sup>365</sup> - 1
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| EAR = '''5.2424%'''.
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| == See also ==
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| * [[ACT/365 fixed]]
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| * [[Annual effective rate]]
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| * [[Annual effective yield]]
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| * [[Annual percentage rate]]
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| * [[Capital market]]
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| * [[Certificate in Treasury Fundamentals]]
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| * [[Certificate in Treasury]]
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| * [[Continuously compounded rate of return]]
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| * [[Effective annual yield]]
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| * [[Equivalent Annual Rate]]
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| * [[LIBOR]]
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| * [[Nominal annual rate]]
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| * [[Periodic discount rate]]
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| * [[Periodic rate of interest]]
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| * [[Periodic yield]]
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| * [[Rate of return]]
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| * [[Real]]
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| * [[Return]]
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| * [[Semi-annual rate]]
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