Mathematics for FinanceMTP Dec 23 Series IIQuestion 3954 of 507
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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.

Options

A135678\displaystyle 135678
B136587\displaystyle 136587
C165878\displaystyle 165878
DNone of these
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Correct Answer

✅ Option d — None of these

All Options:

  • A135678\displaystyle 135678
  • B136587\displaystyle 136587
  • C165878\displaystyle 165878
  • DNone of these

Detailed Solution & Explanation

To find the amount to be paid after 3\displaystyle 3 years, we use the formula for compound interest with successive interest rates: A=P(1+r1100)(1+r2100)(1+r3100)A = P \left(1 + \frac{r_1}{100}\right) \left(1 + \frac{r_2}{100}\right) \left(1 + \frac{r_3}{100}\right) Given parameters: * Principal (P\displaystyle P) = Rs. 1,25,000\displaystyle \text{Rs. }1,25,000 * Rate for 1st year (r1\displaystyle r_1) = 2%\displaystyle 2\% p.a. * Rate for 2nd year (r2\displaystyle r_2) = 3%\displaystyle 3\% p.a. * Rate for 3rd year (r3\displaystyle r_3) = 4%\displaystyle 4\% p.a. Substituting the values into the formula: A=1,25,000×(1+2100)×(1+3100)×(1+4100)A = 1,25,000 \times \left(1 + \frac{2}{100}\right) \times \left(1 + \frac{3}{100}\right) \times \left(1 + \frac{4}{100}\right) A=1,25,000×1.02×1.03×1.04A = 1,25,000 \times 1.02 \times 1.03 \times 1.04 Let's calculate step-by-step: 1,25,000×1.02=1,27,5001,25,000 \times 1.02 = 1,27,500 1,27,500×1.03=1,31,3251,27,500 \times 1.03 = 1,31,325 1,31,325×1.04=1,36,5781,31,325 \times 1.04 = 1,36,578 Since the amount Rs. 1,36,578\displaystyle \text{Rs. }1,36,578 is not listed in Options A, B, or C, Option D ("None of these") is the correct choice. Hence, **Option D** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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.

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:

If an amount is kept at S. I. it earns an interest of Rs. 600\displaystyle \text{Rs. }600 in first two years but when kept at compound interest it earns an interest of Rs. 660\displaystyle \text{Rs. }660 for the same period, then the rate of interest and principal amount respectively are:

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