1. For a sum of money interested at 4% compounded semi-annually for 5 years.
a. the nominal annual rate of interest (j).
b. The number of compounding periods per year (m).
The periods rate of interest (i)
d. The number of compounding periods in the term (n)
e. The compounding factors (1+i)"
f. The numerical value of the compounding factors.
Answers
Given : a sum of money interested at 4% compounded semi-annually for 5 years.
To find : a. the nominal annual rate of interest
b. The number of compounding periods per year
c) The periods rate of interest
d. The number of compounding periods in the term
e. The compounding factors
f. The numerical value of the compounding factors.
Solution:
P = P
R = 4 % annual compounded semi-annually
The number of compounding periods per year = 2
The periods rate of interest = 4/2 = 2 %
( 1 + 2/100)² = ( 1 + r/100)
=> 1.0404 = 1 + r/100
=> r = 4.04 % nominal annual rate of interest
The number of compounding periods in the term
5 years = 10 half years
n = 10
compounding factors = ( 1 + 2/100) = 1.02
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