Mathematics of FinanceMCQPYQ Nov 19Question 1295 of 512
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A trust fund has invested 30,000\displaystyle 30,000 in two different types of bonds which pays 5%\displaystyle 5\% and 7%\displaystyle 7\% interest respectively. Determine how much amount is invested in second type of bond if trust obtains an annual total interest of 1600\displaystyle 1600.

Options

A5000\displaystyle 5000
B6000\displaystyle 6000
C7000\displaystyle 7000
D8000\displaystyle 8000
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Correct Answer

Option a5000\displaystyle 5000

All Options:

  • A5000\displaystyle 5000
  • B6000\displaystyle 6000
  • C7000\displaystyle 7000
  • D8000\displaystyle 8000

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Detailed Solution & Explanation

**Derivation of Invested Sum in Bond Type 2** Given: - Total trust fund = Rs. 30,000\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 \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 (30,000x)\displaystyle (30,000 - x). **Step 2: Set up the annual interest equation** 0.05x+0.07(30000x)=16000.05 x + 0.07(30000 - x) = 1600 0.05x+21000.07x=16000.05 x + 2100 - 0.07 x = 1600 0.02x=16002100-0.02 x = 1600 - 2100 0.02x=500-0.02 x = -500 x=5000.02=Rs. 25,000x = \frac{500}{0.02} = \text{Rs. }25,000 **Step 3: Solve for the amount invested in the second bond** Investment in Bond Type 2=30000x=3000025000=Rs. 5,000\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

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