Mathematics of FinanceMCQPYQ 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 a6,160\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

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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=1,02,0001.88609454,080x = \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=1,08,1601,02,000=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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

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