Question

find the effective rate of interest of 10% p.a payable half yearly​

Answer 1

The effective rate corresponding to 10% p.a. convertible quarterly is 10.4%.

Explanation:

The effective annual interest rate is the interest rate which is actually earned or paid on any financial product as a result of compounding over a given time period. This is also called effective rate or effective Interest rate or annual equivalent rate.

This is expressed as :

Effective rate, E = [1 + i/n]ⁿ – 1

Where

i = nominal interest rate  

n = no. of compounding periods per year

Here we are asked to find the effective rate corresponding to 10% p.a. which is compounded quarterly i.e., n = 4.

Therefore, based on the above formula, we get

E = [1 + (10%/4)]⁴ – 1  

⇒ E = [1 + 0.025]⁴ – 1

⇒ E = [1.025]⁴ – 1

⇒ E = 1.1038 – 1

⇒ E = 0.1038

⇒ E = 10.38% ≈ 10.4%

Thus, the effective rate is 10.4%.