The effective rate corresponding to 10% p.a. convertible quarterly is
(a) 40% (b) 10.1% (c) 10.4% (d) none of these
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Answers
The effective rate corresponding to 10% p.a. convertible quarterly is option (c): 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%.
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