Calculating effective annual rates
Effective annual rate (EAR) is 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
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 period fits into a calendar year
EAR from semi-annual quote
We can calculate EAR from a semi-annual (half-year) quote.
Example 1: 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 from a USD overnight quote which has a 360-day year.
Example 2: 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 rate
- Effective annual yield
- Equivalent Annual Rate
- Nominal annual rate
- Periodic discount rate
- Periodic rate of interest
- Periodic yield
- Rate of return
- Real
- Return
- Semi-annual rate
- SONIA
