For the nominal rate of 18% p.a.
[given that : \( (1.09)^{2}=1.1881,\ (1.045)^{4}=1.1925,\ (1.015)^{12}=1.1956 \)]
Match List-I with List-II
| List-I | List-II | ||
| Nominal rate Compounded | Effective 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:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (III), (B) - (I), (C) - (IV), (D) - (II)
For a nominal rate i compounded m times a year, the effective rate is
\( \displaystyle r_{e}=\left(1+\frac{i}{m}\right)^{m}-1 \)
with i = 0.18 here.
(A) Annually (m = 1)
This matches (III) 18%: compounding once a year, the effective rate equals the nominal rate.
(B) Semi-annually (m = 2)
This matches (I) 18.81%:
\( \displaystyle (1.09)^{2}-1=1.1881-1 \)
\( \displaystyle =0.1881 \)
(C) Quarterly (m = 4)
This matches (IV) 19.25%:
\( \displaystyle (1.045)^{4}-1=1.1925-1 \)
\( \displaystyle =0.1925 \)
(D) Monthly (m = 12)
This matches (II) 19.56%:
\( \displaystyle (1.015)^{12}-1=1.1956-1 \)
\( \displaystyle =0.1956 \)
So the matching is (A)-(III), (B)-(I), (C)-(IV), (D)-(II).
Tip: For the same nominal rate, the effective rate rises with the frequency of compounding, so the order 18% < 18.81% < 19.25% < 19.56% gives the matching directly.