Effective annual rate: Difference between revisions

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imported>Doug Williamson
(Underline 'equivalent', link with ACT/365 fixed page & apply Wiki headings.)
imported>Doug Williamson
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===Conversion formulae===
==Conversion formulae==


r = R / n
r = R / n
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===<span style="color:#4B0082">Example 1: EAR from overnight quote</span>===
<span style="color:#4B0082">'''Example 1: EAR from overnight quote'''</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.
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==Calculate EAR from semi-annual quote==


===<span style="color:#4B0082">Example 2: EAR from semi-annual quote</span>===
We can calculate EAR from a semi-annual (half-year) quote.
 
 
<span style="color:#4B0082">'''Example 2: EAR from semi-annual quote'''</span>


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.
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.
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EAR = '''5.0625%'''.
EAR = '''5.0625%'''.


==Calculate EAR from USD overnight quote==
We can calculate EAR using USD overnight quote which has a 360-day year.




===<span style="color:#4B0082">Example 3: EAR from USD overnight quote (360-day year)</span>===
<span style="color:#4B0082">'''Example 3: EAR from USD overnight quote'''</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.

Revision as of 12:36, 2 December 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: 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%.


Calculate 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%.


Calculate 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