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Mr.Pinto invests one-fifth of his capital at \(6\%\),one-third at \(10\%\) and the remaining at \(1\%\),each rate being simple interest per annum.Then,the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Updated On: Jan 15, 2026
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Solution and Explanation

Let Mr. Pinto's initial capital be \( C \) dollars.

  • He invests \( \frac{1}{5}C \) at \( 6\% \) interest
  • He invests \( \frac{1}{3}C \) at \( 10\% \) interest
  • The remaining amount, \( C - \left( \frac{1}{5}C + \frac{1}{3}C \right) = \frac{11}{15}C \), is invested at \( 1\% \) interest

Interest Accrued After \( t \) Years

The total interest accumulated over \( t \) years is calculated as:

\[ \text{Interest} = \left( \frac{1}{5}C \cdot 0.06 \cdot t \right) + \left( \frac{1}{3}C \cdot 0.10 \cdot t \right) + \left( \frac{11}{15}C \cdot 0.01 \cdot t \right) \]

This accumulated interest must be at least equal to the initial capital \( C \):

\[ \left( \frac{1}{5} \cdot 0.06 + \frac{1}{3} \cdot 0.10 + \frac{11}{15} \cdot 0.01 \right)t \geq 1 \]

 Simplifying the Inequality

Calculating each component of the inequality:

\[ \frac{1}{5} \cdot 0.06 = 0.012,\quad \frac{1}{3} \cdot 0.10 = 0.0333,\quad \frac{11}{15} \cdot 0.01 \approx 0.0073 \]

Summing these values:

\[ 0.012 + 0.0333 + 0.0073 = 0.0526 \]

The simplified inequality is:

\[ 0.0526t \geq 1 \Rightarrow t \geq \frac{1}{0.0526} \approx 19.01 \]

 Final Answer

As the number of years must be a whole number, the minimum number of years required is:

\[ \boxed{20 \text{ years}} \]

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