imported>Doug Williamson |
imported>Doug Williamson |
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| (EAR). | | (IBRD). |
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| | One of five institutions that make up the World Bank Group. |
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| | The IBRD aims to reduce poverty in middle-income countries and creditworthy poorer countries by promoting sustainable development through loans, guarantees, risk management products, and analytical and advisory services. |
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| A quoting convention under which interest at the quoted effective annual rate is calculated and added to the principal annually.
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| EAR is the most usual conventional quotation basis for instruments with maturities of greater than one year.
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| A conventional measure which usefully expresses the returns on different instruments on a comparable basis.
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| 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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| ====Nominal annual rate to periodic rate====
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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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| ====Periodic interest rate or yield to Effective annual rate====
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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 interest calculation period fits into a calendar year of 365 days (or 366 days in a leap year)
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| ==Calculating EAR from overnight quotes==
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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 fixed year.
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| So GBP overnight interest quoted at R = 5.11% means:
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| (i)
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| Interest of:
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| r = R / n
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| r = 5.11% / 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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| <span style="color:#4B0082">'''Example 2: EAR from 360-day overnight quote'''</span>
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| USD short term 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 = 5.11% means:
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| (i)
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| Interest of:
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| r = R / n
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| r = 5.11% / 360
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| r = 0.01419444% (= 0.0001419444) 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 + 0.0001419444 = 1.0001419444
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| EAR = (1 + r)<sup>n</sup> - 1
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| EAR = 1.0001419444<sup>365</sup> - 1
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| EAR = '''5.3171%'''.
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| <span style="color:#4B0082">'''Example 3: EAR in a leap year'''</span>
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| The strict calculation of the effective annual rate is based on the prevailing calendar year, which is 365 days in a normal year, and 366 days in a leap year.
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| For the same periodic rate of interest (r), the effective annual rate is greater in a leap year.
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| For example, where (r) = 0.00014 overnight (as in Example 1).
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| The number of times (n) that the one-day period fits into the calendar year in a leap year = 366.
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| EAR = (1 + r)<sup>n</sup> - 1
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| EAR = 1.00014<sup>366</sup> - 1
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| EAR = '''5.2572%'''.
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| == See also == | | == See also == |
| * [[AER]] | | * [[European Bank for Reconstruction and Development]] |
| * [[ACT/365 fixed]] | | * [[Frontier market]] |
| * [[Annual effective rate]]
| | * [[Organisation for Economic Co-operation and Development]] |
| * [[Annual effective yield]]
| | * [[World Bank]] |
| * [[Annual percentage rate]]
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| * [[Calculating effective annual rates]]
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| * [[Capital market]]
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| * [[Certificate in Treasury Fundamentals]] | |
| * [[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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| * [[Leap year]]
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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]] | |
| * [[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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