Mathematics of FinanceMCQMTP Mar 21Question 1315 of 512
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The difference between the simple and compound interest on a certain sum for 3\displaystyle 3 year at 5%\displaystyle 5\% p.a. is 228.75\displaystyle 228.75. The compound interest on the sum for 2\displaystyle 2 years at 5%\displaystyle 5\% p.a. 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. 228.75\displaystyle \text{Rs. }228.75 **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] 228.75=P[3(0.05)2+(0.05)3]228.75 = P \left[ 3(0.05)^2 + (0.05)^3 \right] 228.75=P[3(0.0025)+0.000125]228.75 = P \left[ 3(0.0025) + 0.000125 \right] 228.75=P[0.0075+0.000125]228.75 = P [ 0.0075 + 0.000125 ] 228.75=0.007625P228.75 = 0.007625 P P=228.750.007625=Rs. 30,000P = \frac{228.75}{0.007625} = \text{Rs. }30,000 **Step 2: Calculate the Compound Interest for 2 years (CI2\displaystyle CI_2) on this Principal** CI2=P[(1+r)21]CI_2 = P \left[ (1 + r)^2 - 1 \right] CI2=30000[(1.05)21]CI_2 = 30000 \left[ (1.05)^2 - 1 \right] CI2=30000[1.10251]CI_2 = 30000 [ 1.1025 - 1 ] CI2=30000×0.1025=Rs. 3,075CI_2 = 30000 \times 0.1025 = \text{Rs. }3,075 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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