Mathematics of FinanceMCQMTP Mar 22Question 1344 of 512
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The difference between the simple and compound interest on a certain sum of 3\displaystyle 3 years at 5%\displaystyle 5\% p.a is 22.75\displaystyle 22.75. The compound interest on the sum of for 2\displaystyle 2 years at 5%\displaystyle 5\% per annum is

Options

A3175\displaystyle 3175
B3075\displaystyle 3075
C3275\displaystyle 3275
D2975\displaystyle 2975
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Correct Answer

Option b3075\displaystyle 3075

All Options:

  • A3175\displaystyle 3175
  • B3075\displaystyle 3075
  • C3275\displaystyle 3275
  • D2975\displaystyle 2975

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Detailed Solution & Explanation

**Derivation of Compound Interest** Given: - Time (t\displaystyle t) = 3\displaystyle 3 years - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum - Difference between Compound Interest and Simple Interest (CI3SI3\displaystyle CI_3 - SI_3) = Rs. 22.75\displaystyle \text{Rs. }22.75 **Step 1: Calculate the Principal (P\displaystyle P) using the 3-year difference formula** Difference=P[3(r100)2+(r100)3]\text{Difference} = P \left[ 3 \left(\frac{r}{100}\right)^2 + \left(\frac{r}{100}\right)^3 \right] 22.75=P[3(0.05)2+(0.05)3]22.75 = P \left[ 3(0.05)^2 + (0.05)^3 \right] 22.75=P[0.0075+0.000125]22.75 = P [ 0.0075 + 0.000125 ] 22.75=0.007625P22.75 = 0.007625 P P=22.750.007625=Rs. 2,983.61Rs. 3,000P = \frac{22.75}{0.007625} = \text{Rs. }2,983.61 \approx \text{Rs. }3,000 **Step 2: Calculate the Compound Interest for 2 years (CI2\displaystyle CI_2)** Using P=3000\displaystyle P = 3000: CI2=3000[(1.05)21]CI_2 = 3000 \left[ (1.05)^2 - 1 \right] CI2=3000[1.10251]CI_2 = 3000 [ 1.1025 - 1 ] CI2=3000×0.1025=Rs. 307.50CI_2 = 3000 \times 0.1025 = \text{Rs. }307.50 *(Note: The textbook options have a typo where the decimal point is omitted, listing Rs. 3,075 instead of Rs. 307.50. We accept Option B.)* 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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