Mathematics of FinanceMCQPYQ Nov 19Question 1295 of 512
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A trust fund has invested $30,000$ in two different types of bonds which pays $5\%and\displaystyle and7\%$ interest respectively. Determine how much amount is invested in second type of bond if trust obtains an annual total interest of $1600$.

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

✅ Option a — $5000$

All Options:

  • A$5000$
  • B$6000$
  • C$7000$
  • D$8000$

Detailed Solution & Explanation

**Derivation of Invested Sum in Bond Type 2** Given: - Total trust fund = Rs. 30,000\displaystyle Rs. \displaystyle \text{Rs. }30,000 - Interest rate of first bond = 5%\displaystyle 5\% per annum - Interest rate of second bond = 7%\displaystyle 7\% per annum - Total annual interest received = Rs. 1,600\displaystyle Rs. \displaystyle \text{Rs. }1,600 **Step 1: Set up the variables** Let x\displaystyle x be the amount invested in the first bond (5%\displaystyle 5\%). Then, the amount invested in the second bond (7%\displaystyle 7\%) is (30,000−x)\displaystyle (30,000 - x). **Step 2: Set up the annual interest equation** 0.05x+0.07(30000−x)=16000.05 x + 0.07(30000 - x) = 1600 0.05x+2100−0.07x=16000.05 x + 2100 - 0.07 x = 1600 −0.02x=1600−2100-0.02 x = 1600 - 2100 −0.02x=−500-0.02 x = -500 x=5000.02=Rs. 25,000x = \displaystyle \frac{500}{0.02} = \text{Rs. }25,000 **Step 3: Solve for the amount invested in the second bond** Investment in Bond Type 2=30000−x=30000−25000=Rs. 5,000\displaystyle \text{Investment in Bond Type 2} = 30000 - x = 30000 - 25000 = \text{Rs. }5,000 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

Exam Strategy Tip

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