Effective annual rate: Difference between revisions
imported>Doug Williamson (Expand in incorporate 'equivalent annual rate'.) |
imported>Doug Williamson (Give examples of conventional year lengths - 360 days or 365 days.) |
||
| Line 14: | Line 14: | ||
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. | 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'.) | ''(For this reason, 'EAR' is sometimes expressed as 'equivalent annual rate'.)'' | ||
| Line 28: | Line 28: | ||
R = nominal annual rate | R = nominal annual rate | ||
n = number of times the period fits into a conventional year | n = number of times the period fits into a conventional year (for example, 360 or 365 days) | ||
| Line 47: | Line 47: | ||
<span style="color:#4B0082">'''Example 1'''</span> | <span style="color:#4B0082">'''Example 1'''</span> | ||
GBP overnight interest is conventionally quoted on a simple interest basis for a 365 day year. | 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: | So GBP overnight interest quoted at R = 5.11% means: | ||
| Line 109: | Line 109: | ||
<span style="color:#4B0082">'''Example 3'''</span> | <span style="color:#4B0082">'''Example 3'''</span> | ||
USD overnight interest is conventionally quoted on a simple interest basis for a 360 day year. | 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: | So USD overnight interest quoted at R = 5.04% means: | ||
Revision as of 12:30, 20 November 2015
(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
Example 1
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%.
Example 2
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%.
Example 3
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
- 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
