Mathematics for FinanceMTP Apr 21, ICAI SMQuestion 1322 of 512
All Questions

A sum of money amounts to 20,800\displaystyle 20,800 in 5\displaystyle 5 years and 22720\displaystyle 22720 in 7\displaystyle 7 years. Find the principle and rate of interest.

Options

A5000,6%\displaystyle 5000, 6\%
B16000,8%\displaystyle 16000, 8\%
C80000,8%\displaystyle 80000, 8\%
D10000,10%\displaystyle 10000, 10\%
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Correct Answer

✅ Option b — 16000,8%\displaystyle 16000, 8\%

All Options:

  • A5000,6%\displaystyle 5000, 6\%
  • B16000,8%\displaystyle 16000, 8\%
  • C80000,8%\displaystyle 80000, 8\%
  • D10000,10%\displaystyle 10000, 10\%

Detailed Solution & Explanation

**Derivation of Principal and Rate of Simple Interest** Given: - Amount in 5\displaystyle 5 years (A5\displaystyle A_5) = Rs. 20,800\displaystyle \text{Rs. }20,800 - Amount in 7\displaystyle 7 years (A7\displaystyle A_7) = Rs. 22,720\displaystyle \text{Rs. }22,720 **Step 1: Calculate Simple Interest for 2 years (SI2\displaystyle SI_2)** SI2=A7−A5=22720−20800=Rs. 1,920SI_2 = A_7 - A_5 = 22720 - 20800 = \text{Rs. }1,920 **Step 2: Calculate Simple Interest for 1 year (SI1\displaystyle SI_1)** SI1=19202=Rs. 960SI_1 = \frac{1920}{2} = \text{Rs. }960 **Step 3: Calculate the Principal (P\displaystyle P)** P=A5−(5×SI1)=20800−(5×960)=20800−4800=Rs. 16,000P = A_5 - (5 \times SI_1) = 20800 - (5 \times 960) = 20800 - 4800 = \text{Rs. }16,000 **Step 4: Calculate the Rate of Interest (R\displaystyle R)** SI1=P×R×1100SI_1 = \frac{P \times R \times 1}{100} 960=16000×R×1100960 = \frac{16000 \times R \times 1}{100} 960=160R  ⟹  R=960160=6% per annum960 = 160 R \implies R = \frac{960}{160} = 6\% \text{ per annum} *(Note: The exam option B (16000,8%\displaystyle 16000, 8\%) has a typo listing 8% instead of 6%. The principal of 16,000 uniquely identifies Option B as correct).* Hence, **Option B** is the correct answer.

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