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Find the EAR In each of the following cases

Finance Sep 11, 2020

Find the EAR In each of the following cases. 

(a) 10% annual interest, compounded quarterly 
(b) 15% annual interest, compounded monthly 
(c) 15% annual interest, compounded daily 
(d) 16% annual interest, with infinite (continuous) compounding.

Expert Solution

a). Computation of the EAR:-

EAR = (1+APR/n)^n-1

Here,

APR = 10%

n = 4 periods (quarterly)

EAR = (1+10%/4)^4-1

= 1.1038 - 1

= 10.38%

 

b). Computation of the EAR:-

EAR = (1+APR/n)^n-1

Here,

APR = 15%

n = 12 periods (monthly

EAR = (1+15%/12)^12-1

= 1.1608 - 1

= 16.08%

 

c). Computation of the EAR:-

EAR = (1+APR/n)^n-1

Here,

APR = 15%

n = 365 periods (compounding daily)

EAR = (1+15%/365)^365-1

= 1.1618 - 1

= 16.18%

 

d). Computation of the EAR:-

EAR = e^rt - 1

Here,

T = Infinite (continuous compounding)

e = 2.7183

EAR = 2.7183^16% - 1

= 1.1735 - 1

= 17.35%

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