a Gold Bo x t Review a x G treasure x -Buy carc Wholesa/X t chargers x zy 24. Ar

Question

a Gold Bo x t Review a x G treasure x -Buy carc Wholesa/X t chargers x zy 24. Arith X-Syllabus x D AGS 200 x D Module: X Chap 6s x a Amazon. X CSecure https:/n Check my work mode: This shows whet is correct or incorrect for the work you have completed so far. It does not indicate completion. Return to question 4 Find the EAR in each of the following cases (Use 365 days a year. Do not round intermediete calculations and enter your enswers as e percent rounded to 2 decimel places, e.g.. 32.16.) 10 olnts Answer is complete but not entirely correct. Stated Rate Number of Times Effective Rate 9.6 1% 10.6 14.6 11.6 Quarterly Monthly Daiy Infinite 877 : 36 1897 14 45 11.07 Pte 4 of 10 Next > Module 1 Task 3..o chapoo1.pdf Show l X

Explanation / Answer

Solution:

The formula for calculating the Effective Annual Rate = ( 1 + i/n ) n   - 1

Where i = Stated rate or nominal Interest rate

             n = Number of compounding periods

(i) As per the information given in the question

Stated rate = 9.6 % = 0.096 and the Number of times compounded = Quarterly = 4 ;

Applying the above values in the formula we have

= ( 1 + ( 0.096/ 4))4 - 1

= (1 + 0.0240 ) 4 - 1 = ( 1.0240 ) 4 – 1

= ( 1.0995 – 1 ) = 0.0995 = 9.95 %

Thus the Effective annual rate when the stated rate = 9.6 % with quarterly compounding = 9.95 %

Note : (1.0240) 4 is calculated in excel using the formula =POWER(1.0240,4)

(ii) As per the information given in the question

Stated rate = 18.6 % = 0.186 and the Number of times compounded = Monthly = 12 ;

Applying the above values in the formula we have

= ( 1 + ( 0.186/ 12))12 - 1

= (1 + 0.0155 )12 - 1 = (1.0155 )12 - 1 =

= ( 1.2027 – 1 ) = 0.2027 = 20.27 %

Thus the Effective annual rate when the stated rate = 18.6 % with monthly compounding = 20.27 %

Note : ( 1.0155 ) 12 is calculated in excel using the formula =POWER(1.0155,12)

(iii) As per the information given in the question

Stated rate = 14.6 % = 0.146 and the Number of times compounded = Daily = 365 ;

Applying the above values in the formula we have

= ( 1 + ( 0.146/ 365))365 - 1

= (1 + 0.0004 )365 - 1 = (1.0004 )365 - 1

= ( 1.1572 – 1 ) = 0.1572 = 15.72 %

Thus the Effective annual rate when the stated rate = 14.6 % with daily compounding = 15.72 %

Note : ( 1.0004 ) 365 is calculated in excel using the formula =POWER(1.0004,365)

(iv) The formula for calculating the Effective annual rate for infinite compounding or continuous compounding is

EAR = e i * n - 1

Where e = a mathematical constant which approximates to 2.7183

i = stated rate ; t= time in years = 1 , since we are calculating effective annual rate

As per the information given in the question

Stated rate = 11.6 % = 0.116 and t = 1

Thus EAR when the compounding is infinite or continuous is = ( 2.7183 )0.116 * 1 - 1

= ( 2.7183 )0.116 - 1

= 1.1230 – 1 = 0.1230 = 12.30 %

Thus the Effective annual rate when the stated rate = 11.6 % with infinite compounding = 12.30 %

Note : ( 2.7183 ) 0.116 is calculated in excel using the formula =POWER(2.7183,0.116)

Thus the final solution is as follows :

Stated Rate               

Number of times compounded

Effective annual rate

9.6 %

Quarterly

9.95 %

18.6 %

Monthly

20.27 %

14.6 %

Daily

15.72 %

11.6 %

Infinite

12.30 %

Stated Rate               

Number of times compounded

Effective annual rate

9.6 %

Quarterly

9.95 %

18.6 %

Monthly

20.27 %

14.6 %

Daily

15.72 %

11.6 %

Infinite

12.30 %

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