Mathematics of FinanceMCQMTP Apr 21Question 1321 of 512
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Two equal sums were lent out at 7%\displaystyle 7\% and 5%\displaystyle 5\% simple interest respectively. The interest earned on the two loans adds up to $960$ for four years. Find the total sum lent out.

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — $4000$

All Options:

  • A$4000$
  • B$3000$
  • C$5000$
  • D$6000$

Detailed Solution & Explanation

**Derivation of Total Sum Lent Out** Given: - Two equal sums P\displaystyle P are lent out. - Rate for first sum (r1\displaystyle r_1) = 7%\displaystyle 7\% p.a. - Rate for second sum (r2\displaystyle r_2) = 5%\displaystyle 5\% p.a. - Time (t\displaystyle t) = 4\displaystyle 4 years - Sum of interests earned = Rs. 960\displaystyle Rs. \displaystyle \text{Rs. }960 **Step 1: Express total interest in terms of P\displaystyle P** Total Interest=SI1+SI2Total Interest=SI1+SI2\displaystyle \text{Total Interest} = SI_1 + SI_2 960=P×7×4100+P×5×4100960 = \displaystyle \frac{P \times 7 \times 4}{100} + \frac{P ×\displaystyle \times 5 ×\displaystyle \times 4}{100} 960=28P100+20P100960 = \displaystyle \frac{28 P}{100} + \frac{20 P}{100} 960=48P100960 = 48P100\displaystyle \frac{48 P}{100} 960=0.48P960 = 0.48 P **Step 2: Solve for P\displaystyle P** P=9600.48=Rs. 2,000P = \displaystyle \frac{960}{0.48} = \text{Rs. }2,000 **Step 3: Calculate the total sum lent out** Total Sum Lent=P+P=2000+2000=Rs. 4,000\displaystyle \text{Total Sum Lent} = P + P = 2000 + 2000 = \text{Rs. }4,000 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.

View Official ICAI Syllabus

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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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