Answer:
a) 12%
b) 12.36%
c) 12.55%
d) 12.68%
Explanation:
Data provided in the question:
Nominal rate of return, r = 12% = 0.12
Now,
Effective rate of interest is given as :
i = [ 1 + ( r ÷ n ) ]ⁿ - 1
here,
Number of compounding periods = n
Thus,
a) compounded annually %
n = 1
i = [ 1 + (0.12 ÷ 1 )]¹ - 1
= 1.12¹ - 1
= 0.12 or 12%
b) compounded semiannually %
n = 2
i = [ 1 + ( 0.12 ÷ 2 ) ]² - 1
= 1.06² - 1
= 0.1236 or 12.36%
c) compounded quarterly %
n = 4
i = [ 1 + ( 0.12 ÷ 4 ) ]⁴ - 1
= 1.03³ - 1
= 0.1255 or 12.55%
(d) compounded monthly %
n = 12
i = [ 1 + ( 0.12 ÷ 12 ) ]¹² - 1
= 1.01¹² - 1
= 0.1268 or 12.68%
