Question

What is the effective annual rate if a bank charges you 8.25 percent compounded quarterly?

a. 8.42%

b. 8.32%

c. 8.51%

d. 8.91%

Answer 1

Solution:

The formula for calculating the Effective annual rate is

EAR = [ [ 1 + ( r / n) ] ⁿ ] -1

Where

r = rate of interest charged ;
n = No. of compounding periods in one year = 12 / Compounding period ;  

As per the information given in the question we have

r = 8.25 % = 0.0825 ; compounding period = 3 months ( since compounding is quarterly ) ;

n = 12 / 3 = 4 ;

Applying the above information in the formula we have

= [ [ 1 + ( 0.0825 / 4 ) ] ⁴ ] - 1

= [ 1 + 0.020625 ] ⁴ - 1

= [ 1.020625 ] ⁴ - 1

= 1.085088 – 1

= 0.085088

= 8.5088 %

= 8.51 % ( when rounded off to two decimal places )

Thus the effective annual rate = 8.51 %

The solution is c. 8.51 %