Question

Periodic interest rates. You have a savings account in which you leave the funds for one year without adding to or withdrawing from the account. Which would you rather have: a daily compounded rate of 0.055​%, a weekly compounded rate of 0.355​%, a monthly compounded rate of 1.45​%, a quarterly compounded rater of 4.50​%, a semiannually compounded rate of 7​%, or an annually compounded rate of 15​%?

What is the effective annual rate​ (EAR) of a daily compounded rate of 0.055​%?

_________% ​(Round to two decimal​ places.)

What is the EAR of a weekly compounded rate of 0.355​%?

__________​% ​(Round to two decimal​ places.)

What is the EAR of a monthly compounded rate of 1.45​%?

__________% ​(Round to two decimal​ places.)

What is the EAR of a quarterly compounded rate of 4.50​%?

__________​% ​(Round to two decimal​ places.)

What is the EAR of a semiannually compounded rate of 7​%?

___________​% (Round to two decimal​ places.)

What is the EAR of an annually compounded rate of 15​%?

___________​% ​(Round to two decimal​ places.)

Which periodic rate would you rather have for your savings​ account? ​(Select the best​ response.)

A. Upper A quarterly compounded rate of 4.50%.

B. Upper A monthly compounded rate of 1.45%.

C. An annually compounded rate of 15%.

D. Upper A daily compounded rate of 0.055%.

E. Upper A weekly compounded rate of 0.355%.

F. Upper A semiannually compounded rate of 7%.

Answer 1

Daily: Periodic Rate = 0.055 %, Number of Periods in a Year = 365

Effective Annual Rate = [1+Periodic Rate]^(Number of Periods in a Year) - 1 = [1.00055]^(365) - 1 = 0.2222 or 22.22 %

Weekly:

Periodic Rate = 0.355 %, Number of Periods in a Year = 52

Effective Annual Rate = [1+Periodic Rate]^(Number of Periods in a Year) - 1 = [1.00355]^(52) - 1 = 0.2023 or 20.23 %

Monthly:

Periodic Rate = 1.45 %, Number of Periods in a Year = 12

Effective Annual Rate = [1+Periodic Rate]^(Number of Periods in a Year) - 1 = [1.0145]^(12) - 1 = 0.1886 or 18.86 %

Quarterly:

Periodic Rate = 4.5 %, Number of Periods in a Year = 4

Effective Annual Rate = [1+Periodic Rate]^(Number of Periods in a Year) - 1 = [1.045]^(4) - 1 = 0.1925 or 19.25 %

Semi-Annual:

Periodic Rate = 7 %, Number of Periods in a Year = 2

Effective Annual Rate = [1+Periodic Rate]^(Number of Periods in a Year) - 1 = [1.07]^(2) - 1 = 0.0.1449 or 14.49 %

Annual:

Periodic Rate = 15 %, Number of Periods in a Year = 1

Effective Annual Rate = [1+Periodic Rate]^(Number of Periods in a Year) - 1 = [1.15]^(1) - 1 = 0.15 or 15 %

As the Effective Annual Rate is highest for daily compounding, the same should be chosen.