This question shows us how the effective rate of a
debt instrument with a nominal yield of 6 percent varies with the number of
payments per year. The effective rate is
also calculated for the case of continuous compounding. The output from the EFFECT function is shown
to be consistent with a formula for the effective rate.
Question: Consider a bond with a nominal yield of 6.0
percent. What is the effective yield on
the bond when the number of yearly payments is 1, 2, 4, 12, or 52?
Some basic concepts:
Nominal Rate  The annual
interest payments divided by the face value of the bond.
The Effective Rate  The
effective rate is the annual rate which corrects for the number of payments per
year on the bond.
Using Excel to Calculate the
Effective Rate:
The calculation using the
Excel Effect function is presented below.
Col A

Col B

Col C

Col D

Nominal Rate

payments per year

Effective rate

Code

6.00%

1

6.000%

"effect(a3,b3)

6.00%

2

6.090%

"effect(a4,b4)

6.00%

4

6.136%

"effect(a5,b5)

6.00%

12

6.168%

"effect(a6,b6)

6.00%

52

6.180%

"effect(a7,b7)

The effective rate can also
be calculated for continuously compounded returns. The formula for this calculation is exp(0.06)1,
which is 6.184%.
The effective rate can also
be calculated without the yield function from the formula r=(1+1/n)^{n}  1
Confirm this formula is
consistent with the EFFECT function. Note that
6.136% = (1+6.0/4)^{4}  1
The next post will look at
effective rates of mortgages with and without posts and with and with and
without prepayment. _{}
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