Effective annual rate
(EAR).
1.
A quoting convention under which interest at the quoted 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 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
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)
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
Calculating EAR from GBP overnight quote
Example 1: 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%.
EAR from semi-annual quote
We can calculate EAR from a semi-annual (half-year) quote.
Example 2: 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 using USD overnight quote which has a 360-day year.
Example 3: 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 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
