Effective annual rate: Difference between revisions
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
- ACT/365 fixed
- Annual effective rate
- Annual effective yield
- Annual percentage rate
- Calculating effective annual rates
- Capital market
- Certificate in Treasury Fundamentals
- Certificate in Treasury
- Continuously compounded rate of return
- 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
