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For the nominal rate of 18 % p.a.

[given that : (1.09)2=1.1881,(1.045)4=1.1925,(1.015)12=1.1956(1.09)^2 = 1.1881, (1.045)^4 = 1.1925, (1.015)^{12} = 1.1956]

Match List-I with List-II

List-IList-II
Nominal rate CompoundedEffective rate
(A) Annually(I) 18.81%
(B) Semi-annually(II) 19.56%
(C) Quarterly(III) 18%
(D) Monthly(IV) 19.25%

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 2

Effective rate =(1+im)m−1=\left(1+\frac{i}{m}\right)^m-1. Annually it stays 18% (III). Semi-annually (1.09)2=1.1881(1.09)^2=1.1881 gives 18.81% (I). Quarterly (1.045)4=1.1925(1.045)^4=1.1925 gives 19.25% (IV). Monthly (1.015)12=1.1956(1.015)^{12}=1.1956 gives 19.56% (II).

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