Mathematics for FinancePYQ May 18Question 1175 of 512
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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:

Options

A1623\displaystyle 16 \frac{2}{3} years
B1614\displaystyle 16 \frac{1}{4} years
C16\displaystyle 16 years
D614\displaystyle 6 \frac{1}{4} years
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Correct Answer

✅ Option a — 1623\displaystyle 16 \frac{2}{3} years

All Options:

  • A1623\displaystyle 16 \frac{2}{3} years
  • B1614\displaystyle 16 \frac{1}{4} years
  • C16\displaystyle 16 years
  • D614\displaystyle 6 \frac{1}{4} years

Detailed Solution & Explanation

**Derivation of Time to Amount to Rs. 2,000** Given: - Initial Principal (P1\displaystyle P_1) = Rs. 1,000\displaystyle \text{Rs. }1,000 - Rate of Interest (r\displaystyle r) = 5%\displaystyle 5\% per annum - Period after which interest is added to principal = 10\displaystyle 10 years **Step 1: Calculate the amount at the end of the first 10\displaystyle 10 years** The simple interest (I1\displaystyle I_1) earned in the first 10\displaystyle 10 years is: I1=P1×r×t1100=1000×5×10100=Rs. 500I_1 = \frac{P_1 \times r \times t_1}{100} = \frac{1000 \times 5 \times 10}{100} = \text{Rs. }500 At the end of 10\displaystyle 10 years, this interest is added to the principal to form the new principal. New Principal (P2\displaystyle P_2) = P1+I1=1000+500=Rs. 1,500\displaystyle P_1 + I_1 = 1000 + 500 = \text{Rs. }1,500 **Step 2: Calculate the time needed for the amount to reach Rs. 2,000** Target Amount = Rs. 2,000\displaystyle \text{Rs. }2,000 Required Interest (I2\displaystyle I_2) in the second period = Target Amount−P2=2000−1500=Rs. 500\displaystyle \text{Target Amount} - P_2 = 2000 - 1500 = \text{Rs. }500 Let t2\displaystyle t_2 be the additional number of years required: I2=P2×r×t2100I_2 = \frac{P_2 \times r \times t_2}{100} 500=1500×5×t2100500 = \frac{1500 \times 5 \times t_2}{100} 500=75×t2500 = 75 \times t_2 t2=50075=203=623 yearst_2 = \frac{500}{75} = \frac{20}{3} = 6\frac{2}{3} \text{ years} **Step 3: Calculate the total time** Total Time=t1+t2=10+623=1623 years\text{Total Time} = t_1 + t_2 = 10 + 6\frac{2}{3} = 16\frac{2}{3} \text{ years} Hence, **Option A** is the correct answer.

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