Mathematics for FinanceMTP Mar 21Question 1314 of 512
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8,000\displaystyle 8,000 becomes 10,000\displaystyle 10,000 in two years at simple interest. The amount that will become 6,875\displaystyle 6,875 in 3\displaystyle 3 years at the same rate of interest is:

Options

A4850\displaystyle 4850
B5000\displaystyle 5000
C5500\displaystyle 5500
D5275\displaystyle 5275
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Correct Answer

✅ Option b — 5000\displaystyle 5000

All Options:

  • A4850\displaystyle 4850
  • B5000\displaystyle 5000
  • C5500\displaystyle 5500
  • D5275\displaystyle 5275

Detailed Solution & Explanation

**Derivation of Principal Amount** Given: - First scenario: Principal (P1\displaystyle P_1) = Rs. 8,000\displaystyle \text{Rs. }8,000 becomes Amount (A1\displaystyle A_1) = Rs. 10,000\displaystyle \text{Rs. }10,000 in t1=2\displaystyle t_1 = 2 years under simple interest. - Second scenario: Future Value (A2\displaystyle A_2) = Rs. 6,875\displaystyle \text{Rs. }6,875 in t2=3\displaystyle t_2 = 3 years at the same rate. **Step 1: Calculate the interest rate (R\displaystyle R) from the first scenario** SI1=A1−P1=10000−8000=Rs. 2,000SI_1 = A_1 - P_1 = 10000 - 8000 = \text{Rs. }2,000 SI1=P1×R×t1100SI_1 = \frac{P_1 \times R \times t_1}{100} 2000=8000×R×21002000 = \frac{8000 \times R \times 2}{100} 2000=160R  ⟹  R=2000160=12.5% per annum2000 = 160 R \implies R = \frac{2000}{160} = 12.5\% \text{ per annum} **Step 2: Calculate the required principal (P2\displaystyle P_2) for the second scenario** A2=P2(1+R×t2100)A_2 = P_2\left(1 + \frac{R \times t_2}{100}\right) 6875=P2(1+12.5×3100)6875 = P_2\left(1 + \frac{12.5 \times 3}{100}\right) 6875=P2(1+0.375)6875 = P_2(1 + 0.375) 6875=1.375P26875 = 1.375 P_2 P2=68751.375=Rs. 5,000P_2 = \frac{6875}{1.375} = \text{Rs. }5,000 Hence, **Option B** is the correct answer.

More Questions from Mathematics for Finance

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A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

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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