Effective annual rate: Difference between revisions
imported>Doug Williamson (Link with related periodic rate pages.) |
imported>Doug Williamson (Expand examples and conversion formula.) |
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'''Example''' | '''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 | |||
EAR = (1 + r)<sup>n</sup> - 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. | GBP overnight interest is conventionally quoted on a simple interest basis for a 365 day year. | ||
So GBP overnight interest quoted at 5.11% means: | So GBP overnight interest quoted at R = 5.11% means: | ||
(i) | |||
Interest of: | |||
r = R / n | |||
r = 5.11% / 365 | |||
r = 0.014% is paid per day. | |||
(ii) | |||
The ''equivalent'' effective annual rate is: | |||
EAR = (1 + r)<sup>n</sup> - 1 | |||
EAR = 1.00014<sup>365</sup> - 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)<sup>n</sup> - 1 | |||
EAR = 1.025<sup>2</sup> - 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) | (i) | ||
Interest of 5. | Interest of: | ||
r = R / n | |||
r = 5.04% / 360 | |||
r = 0.014% is paid per day. | |||
(ii) | (ii) | ||
The ''equivalent'' effective annual rate is | The ''equivalent'' effective annual rate is: | ||
EAR = (1 + r)<sup>n</sup> - 1 | |||
= 1.00014<sup>365</sup> - 1 | EAR = 1.00014<sup>365</sup> - 1 | ||
= 5. | EAR = '''5.2424%'''. | ||
Revision as of 11:01, 27 October 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.
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
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% is paid per day.
(ii)
The equivalent effective annual rate is:
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%.
