Mathematics for FinanceMTP Jun 23 Series IIQuestion 3940 of 507
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1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1\displaystyle 1st year, 3%\displaystyle 3\% for the 2\displaystyle 2nd year and 4%\displaystyle 4\% for the 3\displaystyle 3rd year. Find the amount to be paid after 3\displaystyle 3 years

Options

A125678\displaystyle 125678
B136587\displaystyle 136587
C163378\displaystyle 163378
D136578\displaystyle 136578
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Correct Answer

Option d136578\displaystyle 136578

All Options:

  • A125678\displaystyle 125678
  • B136587\displaystyle 136587
  • C163378\displaystyle 163378
  • D136578\displaystyle 136578

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 the 1st year (r1\displaystyle r_1) = 2%\displaystyle 2\% p.a. * Rate for the 2nd year (r2\displaystyle r_2) = 3%\displaystyle 3\% p.a. * Rate for the 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 Thus, the amount to be paid after 3\displaystyle 3 years is Rs. 1,36,578\displaystyle \text{Rs. }1,36,578. Hence, **Option D** is the correct answer.

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