Question

Do not round intermediate calculations. Final dollar answers should be rounded to two decimal places. Final interest rate answers should be rounded to 4 decimal places if stated as a percentage, and 6 decimal places otherwise. Final answers indicating periods should be rounded up to whole periods.

PLEASE SHOW ALL WORK! WITHOUT FINANCIAL CALCULATOR

a) Given an effective quarterly rate of 2.5%, determine the equivalent effective annual rate.

b) Given an effective annual rate of 9%, determine the equivalent effective monthly rate.

Answer 1

a) Effective quarterly rate = 2.5%

The effective annual rate = (1 + Effective quarterly rate)^4 - 1

The effective annual rate = (1 + 0.025)^4 - 1

The effective annual rate = 1.025^4 - 1

The effective annual rate = 1.1038128906 - 1

The effective annual rate = 0.1038128906

The effective annual rate = 10.38128906%

The effective annual rate = 10.3813%

b) Effective annual rate = 9%

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

Effective monthly rate = (1 + 0.09)^(1/12) - 1

Effective monthly rate = 1.0072073233 - 1

Effective monthly rate = 0.0072073233

Effective monthly rate = 0.72073233%

Effective monthly rate = 0.7207%