Mathematics for FinancePYQ May 18Question 1176 of 512
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A person borrows Rs. 5,000\displaystyle \text{Rs. }5,000 for 2\displaystyle 2 years at 4%\displaystyle 4\% per annual simple interest. He immediately lends to another person at 6.25%\displaystyle 6.25\% per annum for 2\displaystyle 2 years find his gain in the transaction for year:

Options

ARs. 112.50\displaystyle \text{Rs. }112.50
BRs. 125\displaystyle \text{Rs. }125
CRs. 107.50\displaystyle \text{Rs. }107.50
DRs. 102.50\displaystyle \text{Rs. }102.50
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Correct Answer

✅ Option a — Rs. 112.50\displaystyle \text{Rs. }112.50

All Options:

  • ARs. 112.50\displaystyle \text{Rs. }112.50
  • BRs. 125\displaystyle \text{Rs. }125
  • CRs. 107.50\displaystyle \text{Rs. }107.50
  • DRs. 102.50\displaystyle \text{Rs. }102.50

Detailed Solution & Explanation

**Derivation of Gain per Year** Given: - Principal amount (P\displaystyle P) = Rs. 5,000\displaystyle \text{Rs. }5,000 - Borrowing rate of interest (r1\displaystyle r_1) = 4%\displaystyle 4\% per annum - Lending rate of interest (r2\displaystyle r_2) = 6.25%\displaystyle 6.25\% per annum - Time (t\displaystyle t) = 2\displaystyle 2 years **Step 1: Calculate interest paid on borrowing per year** Interest Paid per year=P×r1×1100=5000×4×1100=Rs. 200\text{Interest Paid per year} = \frac{P \times r_1 \times 1}{100} = \frac{5000 \times 4 \times 1}{100} = \text{Rs. }200 **Step 2: Calculate interest received from lending per year** Interest Received per year=P×r2×1100=5000×6.25×1100=Rs. 312.50\text{Interest Received per year} = \frac{P \times r_2 \times 1}{100} = \frac{5000 \times 6.25 \times 1}{100} = \text{Rs. }312.50 **Step 3: Calculate gain per year** Gain per year=Interest Received per year−Interest Paid per year\text{Gain per year} = \text{Interest Received per year} - \text{Interest Paid per year} Gain per year=312.50−200=Rs. 112.50\text{Gain per year} = 312.50 - 200 = \text{Rs. }112.50 Alternatively, the gain rate per year is: Gain Rate=r2−r1=6.25%−4%=2.25% per annum\text{Gain Rate} = r_2 - r_1 = 6.25\% - 4\% = 2.25\% \text{ per annum} Gain per year=5000×2.25×1100=Rs. 112.50\text{Gain per year} = \frac{5000 \times 2.25 \times 1}{100} = \text{Rs. }112.50 Hence, **Option A** is the correct answer.

More Questions from Mathematics for Finance

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Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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