Mathematics for FinancePYQ July 21Question 1449 of 512
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A loan of ₹1,02,000\displaystyle ₹ 1,02,000 is to be paid back in two equal annual instalments. If the rate is 4%\displaystyle 4\% p.a. compounded annually, then the total interest charged under this instalment plan is:

Options

A6,160\displaystyle 6,160
B8,120\displaystyle 8,120
C6,980\displaystyle 6,980
D7,560\displaystyle 7,560
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Correct Answer

✅ Option a — 6,160\displaystyle 6,160

All Options:

  • A6,160\displaystyle 6,160
  • B8,120\displaystyle 8,120
  • C6,980\displaystyle 6,980
  • D7,560\displaystyle 7,560

Detailed Solution & Explanation

Let the equal annual installment be x\displaystyle x. Given parameters: * Loan Amount (PV\displaystyle PV) = Rs. 1,02,000\displaystyle \text{Rs. }1,02,000 * Time (n\displaystyle n) = 2\displaystyle 2 years * Interest Rate (r\displaystyle r) = 4%\displaystyle 4\% p.a., so i=0.04\displaystyle i = 0.04 The formula relating loan amount and installments is: PV=x[11+i+1(1+i)2]PV = x \left[ \frac{1}{1+i} + \frac{1}{(1+i)^2} \right] Substituting the values: 1,02,000=x[11.04+1(1.04)2]1,02,000 = x \left[ \frac{1}{1.04} + \frac{1}{(1.04)^2} \right] 1,02,000=x[0.961538+0.924556]1,02,000 = x \left[ 0.961538 + 0.924556 \right] 1,02,000=1.886094x1,02,000 = 1.886094 x Solving for x\displaystyle x: x=1,02,0001.886094≈54,080x = \frac{1,02,000}{1.886094} \approx 54,080 Total amount paid in two installments = 2×54,080=1,08,160\displaystyle 2 \times 54,080 = 1,08,160. Total interest charged = Total Amount Paid - Loan Amount: Interest=1,08,160−1,02,000=6,160\text{Interest} = 1,08,160 - 1,02,000 = 6,160 Thus, the total interest charged is Rs. 6,160\displaystyle \text{Rs. }6,160. Hence, **Option A** is the correct answer.

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