Find the rate of interest by which a sum will triple itself in 16 years

Let  the rate of interest and sum of money be R % p.a and Rs. P respectively.

Given, A = 3P and T = 16 years

Amount = Principle + S.I.

∴ A = P + S.I.

⇒ S.I. = A – P

$$\begin{gathered} \Rightarrow \mathrm{S}.\mathrm{I}=3\mathrm{P}-\mathrm{P}=2\mathrm{P} \\ \mathrm{So}, \mathrm{S}.\mathrm{I}=\frac{\mathrm{PRT}}{100} \\ \Rightarrow 2\mathrm{P}=\frac{\mathrm{P}\times \mathrm{R}\times 16}{100} \\ \Rightarrow \mathrm{R}=\frac{200}{16} \\ \Rightarrow \mathrm{R}=12.5\% \end{gathered}$$
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