Effective annual rate: Difference between revisions

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imported>Doug Williamson
(Add 'usefully'.)
imported>Doug Williamson
(Expand re: quotation basis, clarify that 366 days are used in a leap year.)
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A quoting convention under which interest at the quoted rate is calculated and added to the principal annually.  
A quoting convention under which interest at the quoted effective annual rate is calculated and added to the principal annually.  


EAR is the most usual conventional quotation basis for instruments with maturities of greater than one year.
EAR is the most usual conventional quotation basis for instruments with maturities of greater than one year.
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For this reason, 'EAR' is sometimes expressed as <u>equivalent</u> annual rate.
For this reason, 'EAR' is sometimes expressed as <u>equivalent</u> annual rate.




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r = periodic interest rate or yield, as before
r = periodic interest rate or yield, as before


n = number of times the period fits into a calendar year
n = number of times the interest calculation period fits into a calendar year of 365 days (or 366 days in a leap year)





Revision as of 11:25, 5 March 2016

(EAR).

1.

A quoting convention under which interest at the quoted effective annual rate is calculated and added to the principal annually.

EAR is the most usual conventional quotation basis for instruments with maturities of greater than one year.


2.

A conventional measure which usefully 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 interest calculation period fits into a calendar year of 365 days (or 366 days in a leap year)


Calculating EAR from GBP overnight quote

Example: EAR from overnight quote

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

So GBP overnight interest quoted at R = 5.11% means:

(i)

Interest of:

r = R / n

r = 5.11% / 365

r = 0.014% (= 0.00014) is paid per day.


(ii)

The equivalent effective annual rate is calculated from (1 + r).

1 + r = 1 + 0.00014 = 1.00014


EAR = (1 + r)n - 1

EAR = 1.00014365 - 1

EAR = 5.2424%.


See also