Question

A special account pays 4.9% nominal interest compounded every 3 months.

a) What is the effective annual rate?

b) What is the effective quarterly rate?

Answer 1

a) Ans:The effective annual rate is 4.9%

b) Ans: The effective quarterly rate is 4.99% or 5%

Explanation:

Effective rate = ( 1 + r/m )^m - 1

Where ,

r = nominal interest rate

m = number of interest period in a year

Annual effective rate;

= ( 1 + r/m )^m - 1

= {1 + (0.049 / 1) }¹ - 1

= ( 1 + 0.049)¹ - 1

= 1.049 -1

= 0.049 or 4.9 %

Quarterly effective rate;

= ( 1 + r/m )^m - 1

= {1 + (0.049 / 4) }⁴ - 1

= ( 1 + 0.01225)⁴ - 1

=( 1.01225)⁴ - 1

= 1.049908 - 1

= 0.049908

= 4. 99 %