A loan of Rs. 1,00,000 at 12% per annum compounded monthly is repaid in 24 equal monthly instalments of Rs. 4,707.35 each, paid at the end of each month, by the reducing balance method. Which of the following statements are correct?
(A) The interest part of the first instalment is Rs. 1,000.
(B) The principal outstanding just after the first instalment is paid is Rs. 96,292.65.
(C) The interest part of every instalment is Rs. 1,000.
(D) The total interest paid over the 2 years is Rs. 24,000.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (B) only
The rate per month is
\( \displaystyle i = \frac{0.12}{12} = 0.01 \)
In the reducing balance method, the interest in each EMI is charged only on the principal still outstanding.
Interest in the first EMI:
\( 100000 \times 0.01 = 1000 \)
Principal repaid by the first EMI:
\( 4707.35 - 1000 = 3707.35 \)
Principal outstanding after the first EMI:
\( 100000 - 3707.35 = 96292.65 \)
Total interest over 24 EMIs:
\( 4707.35 \times 24 - 100000 = 112976.40 - 100000 = 12976.40 \)
So the first interest part is Rs. 1,000, the balance after one EMI is Rs. 96,292.65, the interest part falls with every EMI, and the total interest is Rs. 12,976.40.
Checking the statements
(A) The interest part of the first instalment is Rs. 1,000. — Correct. 1% of Rs. 1,00,000 = 1,000.
(B) The principal outstanding just after the first instalment is paid is Rs. 96,292.65. — Correct. 1,00,000 − 3,707.35 = 96,292.65.
(C) The interest part of every instalment is Rs. 1,000. — Incorrect. The second interest part is 1% of 96,292.65 = Rs. 962.93, so it falls each month.
(D) The total interest paid over the 2 years is Rs. 24,000. — Incorrect. The total interest is 1,12,976.40 − 1,00,000 = Rs. 12,976.40; Rs. 24,000 is the flat rate interest.