Question

11. Which one of the following investments provides the highest effective annual rate of return (i.e., which of the following investments represents the largest EAR), assuming an investor wants to avoid earning the lowest return over an investing 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.

Answer 1

where r = Stated Annual Rate

m = compounding per year

Solution) Option A)

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

m = 1

Effective annual rate = (1 + 3%)^1 - 1 = 1.03 - 1 = 0.03 = 3%

Option B)

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

m = 2

Effective annual rate = (1 + 2.98%/2)^2 - 1

= 3.0022%

Option C)

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

m = 4

Effective annual rate = (1 + 2.965%/4)^4 - 1

= 2.9981%

Option D)

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

m =12

Effective annual rate = (1 + 2.9575%/12)^12 - 1

= 2.9979%

Option E)

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

m = 365

Effective annual rate = (1 + 2.955%/365)^365 - 1

= 2.9990%

From the above options, the effective annual rate is highest for Option B

Hence, the correct option is B.