Question

In: Finance

Which one of the following investments provides the highest effective annual rate of return (i.e., which...

Which one of the following investments provides the highest effective annual rate of return (i.e., which of the following investments is the BEST = the largest EAR) over an investment horizon of 10 years)?

a. An investment which has a 3.0 percent nominal rate with annual compounding.

b. An investment which has a 2.98 percent nominal rate with semi-annual compounding.

c. An investment which has a 2.965 percent nominal rate with quarterly compounding.

d. An investment which has a 2.9575 percent nominal rate with monthly compounding.

e. An investment which has a 2.955 percent nominal rate and daily (365) compounding

Solutions

Expert Solution

b. An investment which has a 2.98 percent nominal rate with semi-annual compounding.

a. Effective annual rate of return = ((1+i)^n)-1 Where,
(EAR) = ((1+0.03)^1)-1 i Nominal rate of return           0.03
= 3.000% n Number of times compounding in a year 1
b. Effective annual rate of return = ((1+(i/n))^n)-1 Where,
(EAR) = ((1+(0.0298/2))^2)-1 i       0.0298
= 3.002% n 2
c. Effective annual rate of return = ((1+(i/n))^n)-1 Where,
(EAR) = ((1+(0.02965/4))^4)-1 i     0.02965
= 2.998% n 4
d. Effective annual rate of return = ((1+(i/n))^n)-1 Where,
(EAR) = ((1+(0.029575/12))^12)-1 i 0.029575
= 2.998% n 12
e. Effective annual rate of return = ((1+(i/n))^n)-1 Where,
(EAR) = ((1+(0.02955/365))^365)-1 i     0.02955
= 2.999% n 365
So,
b. An investment which has a 2.98 percent nominal rate with semi-annual compounding has highest effective annual rate of return.

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