Vatsala buys a car for Rs.7,00,000 and pays upfront Rs.2,50,000 through her credit card. The balance is to be paid in 5 years by equal monthly installments at an interest of 7% per annum as reducing balance. The EMI to be paid by Vatsala will be:- [given \((1.0058)^{-60}=0.7068\)]
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 8901.7
Under the reducing balance method, the EMI on a loan P at rate i per month for n months is
\( \displaystyle E = \frac{P\,i}{1 - (1 + i)^{-n}} \)
The loan is the balance left after the upfront payment:
\(P = 700000 - 250000 = 450000\)
The monthly rate is 7% divided by 12, taken as 0.0058 as in the given value, and the loan runs for 60 months:
\( \displaystyle i = \frac{7}{12 \times 100} \approx 0.0058 \)
\(n = 5 \times 12 = 60\)
Substituting, with \((1.0058)^{-60} = 0.7068\):
\( \displaystyle E = \frac{450000 \times 0.0058}{1 - 0.7068} \)
\( \displaystyle E = \frac{2610}{0.2932} \)
\(E \approx 8901.7\)
So the EMI is about Rs. 8901.7.