A property dealer wishes to buy different houses given in the table below with some down payments and balance in EMI for 25 years. Bank charges 6% per annum compounded monthly.
\(\left(\text{Given } \displaystyle\frac{(1.005)^{300} \times 0.005}{(1.005)^{300} - 1} = 0.0064\right)\)
| Property type | Price of the property (in Rs.) | Down Payment (in Rs.) |
| P | 45,00,000 | 5,00,000 |
| Q | 55,00,000 | 5,00,000 |
| R | 65,00,000 | 10,00,000 |
| S | 75,00,000 | 15,00,000 |
Match List-I with List-II:
| List-I | List-II | ||
| Property Type | EMI amount (in Rs.) | ||
| (A) | P | (I) | 25,600 |
| (B) | Q | (II) | 38,400 |
| (C) | R | (III) | 32,000 |
| (D) | S | (IV) | 35,200 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (I), (B) - (III), (C) - (IV), (D) - (II)
The bank lends the price minus the down payment. With the monthly rate i = 6%/12 = 0.005 and n = 25 × 12 = 300 instalments, the EMI formula is
\( \displaystyle \text{EMI} = \text{Loan} \times \frac{i(1+i)^{n}}{(1+i)^{n} - 1} = \text{Loan} \times 0.0064 \)
(A) P
This matches (I) 25,600.
\(\text{Loan} = 45{,}00{,}000 - 5{,}00{,}000 = 40{,}00{,}000\)
\(\text{EMI} = 40{,}00{,}000 \times 0.0064 = 25{,}600\)
(B) Q
This matches (III) 32,000.
\(\text{Loan} = 55{,}00{,}000 - 5{,}00{,}000 = 50{,}00{,}000\)
\(\text{EMI} = 50{,}00{,}000 \times 0.0064 = 32{,}000\)
(C) R
This matches (IV) 35,200.
\(\text{Loan} = 65{,}00{,}000 - 10{,}00{,}000 = 55{,}00{,}000\)
\(\text{EMI} = 55{,}00{,}000 \times 0.0064 = 35{,}200\)
(D) S
This matches (II) 38,400.
\(\text{Loan} = 75{,}00{,}000 - 15{,}00{,}000 = 60{,}00{,}000\)
\(\text{EMI} = 60{,}00{,}000 \times 0.0064 = 38{,}400\)
So the matching is (A) - (I), (B) - (III), (C) - (IV), (D) - (II).