Mathematics of FinanceMCQPYQ 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 a1623\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

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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 AmountP2=20001500=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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

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