Mr. Bean wishes to purchase a house for Rs. 90,00,000 with a down payment of Rs. 10,00,000 and balance in EMI for 25 years on reducing balance payment basis. If bank charges 6% per annum compounded monthly, then his EMI is;
(Use \( (1.005)^{300}=4.4650 \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 51,544
The loan amount is the price less the down payment:
\( \displaystyle P=90{,}00{,}000-10{,}00{,}000=80{,}00{,}000 \)
Monthly rate and number of instalments:
\( \displaystyle i=\frac{6}{12\times 100}=0.005 \)
\( \displaystyle n=25\times 12=300 \)
EMI on the reducing balance method:
\( \displaystyle EMI=\frac{P\,i\,(1+i)^{n}}{(1+i)^{n}-1} \)
\( \displaystyle =\frac{80{,}00{,}000\times 0.005\times 4.4650}{4.4650-1} \)
\( \displaystyle =\frac{40{,}000\times 4.4650}{3.4650} \)
\( \displaystyle =\frac{1{,}78{,}600}{3.4650} \)
\( \displaystyle \approx 51{,}544 \)
So the EMI is Rs. 51,544.
Why the other options are incorrect
Option (1) Rs. 178600 — Incorrect. Rs. 178600 is only the numerator \( P\,i\,(1+i)^{n} \); it has not been divided by \( (1+i)^{n}-1 \).
Option (3) Rs. 40,000 — Incorrect. Rs. 40,000 = P × i is only the interest for the first month; the EMI must also repay part of the principal.
Option (4) Rs. 52,382 — Incorrect. The EMI works out to about Rs. 51,544, not Rs. 52,382.