Mathematics of FinanceMCQPYQ Jan 21Question 1215 of 512
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Two equal amounts of money are deposited in two banks each at 15%\displaystyle 15\% p.a. 3.5\displaystyle 3.5 year in the bank and for 5\displaystyle 5 years in the other. The difference between the interest amount from the bank in 144\displaystyle 144. Find the sum

Options

A620\displaystyle 620
B640\displaystyle 640
C820\displaystyle 820
D840\displaystyle 840
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Correct Answer

Option b640\displaystyle 640

All Options:

  • A620\displaystyle 620
  • B640\displaystyle 640
  • C820\displaystyle 820
  • D840\displaystyle 840

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Detailed Solution & Explanation

**Derivation of Principal Amount from Difference in Interest** Given: - Equal amounts (P\displaystyle P) deposited in two banks. - Rate of Interest (r\displaystyle r) = 15%\displaystyle 15\% per annum simple interest. - Time periods: t1=3.5\displaystyle t_1 = 3.5 years and t2=5\displaystyle t_2 = 5 years. - Difference between the interests earned (SI2SI1\displaystyle SI_2 - SI_1) = Rs. 144\displaystyle \text{Rs. }144 **Step 1: Set up the Simple Interest difference equation** SI2SI1=P×r×t2100P×r×t1100SI_2 - SI_1 = \frac{P \times r \times t_2}{100} - \frac{P \times r \times t_1}{100} 144=P×15×(t2t1)100144 = \frac{P \times 15 \times (t_2 - t_1)}{100} 144=P×15×(53.5)100144 = \frac{P \times 15 \times (5 - 3.5)}{100} 144=P×15×1.5100144 = \frac{P \times 15 \times 1.5}{100} 144=0.225P144 = 0.225 P **Step 2: Solve for Principal (P\displaystyle P)** P=1440.225=Rs. 640P = \frac{144}{0.225} = \text{Rs. }640 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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