Mathematics for FinanceMTP 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 b — 3075\displaystyle 3075

All Options:

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

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 (CI3−SI3\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)2−1]CI_2 = P \left[ (1 + r)^2 - 1 \right] CI2=30000[(1.05)2−1]CI_2 = 30000 \left[ (1.05)^2 - 1 \right] CI2=30000[1.1025−1]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.

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