Question

21) If a bank pays a 3.5% nominal annual rate, with monthly compounding, on deposits, what effective annual rate does the bank pay? a. 2.02% b. 2.53% c. 3.04% d. 3.56% e. 4.07%

Answer 1

Solution:

The formula for calculating the Effective annual rate is

EAR = [ [ 1 + (NAR/ n) ] ⁿ ] -1

Where

NAR = Nominal Annual Rate
n = No. of compounding periods in one year = 12 / Compounding periods in one year

As per the Information given in the question we have

NAR = 3.5 % = 0.035

Compounding periods = 1 month   ( since compounding is monthly )

n = 12 / 1 = 12

Applying the above values in the formula we have

= [ [ 1 + ( 0.035/12 ) ] ¹² ] -1                 

= [ [ 1 + 0.002917) ] ¹² ] – 1

= [ [ 1.002917) ] ¹² ] – 1

= 1.035567 - 1

= 0.035567

= 3.5567 %

= 3.56 % (when rounded off to two decimal places )

Thus the EAR = 3.56 % when the NAR is 3.5 % with monthly compounding.

Thus the solution is Option d. 3.56 %

Note : ( 1.002917 ) ¹² is calculated using the excel formula =POWER(Number,Power)

= POWER(1.002917,12) = 1.002917