A money-lender charges interest at the rate of 10 rupees per 110 rupees semi-annually, payable in advance. Then
Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| A. | rate per conversion period \( (i) \) | I. | 2 |
| B. | nominal rate (r)% | II. | 21 |
| C. | number of period in a year (m) | III. | 20 |
| D. | effective rate of interest \( (\mathrm{r_e}) \)% | IV. | 0.1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-IV, B-III, C-I, D-II
Interest payable in advance is deducted at the start: out of Rs. 110, the borrower actually receives 110 − 10 = Rs. 100 and repays Rs. 110 after six months. So the interest of Rs. 10 is earned on Rs. 100 in one half-year.
(A) rate per conversion period (i)
This matches (IV) 0.1.
\( \displaystyle i=\frac{10}{100}=0.1\ \text{per half-year} \)
(B) nominal rate (r)%
This matches (III) 20.
\( \displaystyle r=m\times i=2\times 10\%=20\% \)
(C) number of period in a year (m)
This matches (I) 2, since interest is converted semi-annually.
(D) effective rate of interest \( (r_e) \)%
This matches (II) 21.
\( \displaystyle r_e=(1+i)^m-1=(1.1)^2-1 \)
\( \displaystyle =0.21=21\% \)
So the matching is A-IV, B-III, C-I, D-II.
Tip: “Payable in advance” means the interest is subtracted from the sum lent, so the rate is interest ÷ (sum − interest), here 10/100, not 10/110.