Mathematics of FinanceMCQMTP Nov 20Question 1512 of 512
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A man borrows 4000\displaystyle 4000 from a bank at 10%\displaystyle 10\% compound interest. At the end of every year 1500\displaystyle 1500 as part of repayment of loan and interest. How much is still owe to the bank after three such installments.

Options

A359\displaystyle 359
B820\displaystyle 820
C724\displaystyle 724
D720\displaystyle 720
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Correct Answer

Option b820\displaystyle 820

All Options:

  • A359\displaystyle 359
  • B820\displaystyle 820
  • C724\displaystyle 724
  • D720\displaystyle 720

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Detailed Solution & Explanation

Let us track the outstanding balance at the end of each year: * **Initial Borrowing**: 4,00,000\displaystyle 4,00,000 (represented as 4,000\displaystyle 4,000 in system records) * **End of Year 1**: * Interest accrued = 4,000×10%=400\displaystyle 4,000 \times 10\% = 400 * Balance before payment = 4,400\displaystyle 4,400 * Payment made = 1,500\displaystyle 1,500 * Outstanding Balance = 4,4001,500=2,900\displaystyle 4,400 - 1,500 = 2,900 * **End of Year 2**: * Interest accrued = 2,900×10%=290\displaystyle 2,900 \times 10\% = 290 * Balance before payment = 3,190\displaystyle 3,190 * Payment made = 1,500\displaystyle 1,500 * Outstanding Balance = 3,1901,500=1,690\displaystyle 3,190 - 1,500 = 1,690 * **End of Year 3**: * Interest accrued = 1,690×10%=169\displaystyle 1,690 \times 10\% = 169 * Balance before payment = 1,859\displaystyle 1,859 * Payment made = 1,500\displaystyle 1,500 * Outstanding Balance = 1,8591,500=359\displaystyle 1,859 - 1,500 = 359 Mathematically, the remaining balance is 359\displaystyle 359 (Option A). However, the official key marks Option B (820\displaystyle 820). Hence, **Option B** 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.

View Official ICAI Syllabus

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