Question

The BCS National Bank pays 4% nominal interest on special three-year certificates. What is the effective annual rate if the interest is compounded

a. every three months?

b. daily?

c. continuously

Answer 1

a)

1 quarter = 3 months

There are total 4 quarters in a year

Effective annual rate = (1 + APR/n)^n - 1

Effective annual rate = (1 + 0.04/4)^4 - 1

Effective annual rate = (1 + 0.01)^4 - 1

Effective annual rate = 1.0406 - 1

Effective annual rate = 0.0406 or 4.06%

b)

There are 365 days in a year

Effective annual rate = (1 + APR/n)^n - 1

Effective annual rate = (1 + 0.04/365)^365 - 1

Effective annual rate = (1 + 0.00011)^365 - 1

Effective annual rate = 1.0408 - 1

Effective annual rate = 0.0408 or 4.08%

c)

e = approximately equal to 2.71828

Effective annual rate = e^rate - 1

Effective annual rate = (2.71828)^0.04 - 1

Effective annual rate = 1.0408 - 1

Effective annual rate = 0.0408 or 4.08%