Find the effective rate of interest corresponding to a nominal rate of 12%/year compounded in the following ways. (Round your answers to two decimal places.) (a) compounded annually % (b) compounded semiannually % (c) compounded quarterly % (d) compounded monthly %

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%