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Question

A certain sum of money, placed out at compound interest, amounts to Rs.6,272 in 2 years and to Rs. 7,024.64 in 3 years. Find the rate of interest and the sum of money.


Solution

$$We\quad know\quad that\quad Compound\quad Interest=Amount-Principal$$
 $$Amount\quad for\quad 3rd\quad year-Amount\quad for\quad 2nd\quad year\quad will\quad be\quad the\quad interest\quad for\quad 3rd\quad year$$
$$Amount\quad for\quad 2nd\quad year\quad will\quad serve\quad as\quad Principal\quad for\quad 3rd\quad year$$
$$As\quad per\quad problem\quad 7024.64-6272=752.64(compound\quad interest)$$
 $$\Rightarrow P{ \left( 1+\frac { r }{ 100 }  \right)  }^{ 3 }-P{ \left( 1+\frac { r }{ 100 }  \right)  }^{ 2 }=752.64$$
 $$\Rightarrow P{ \left( 1+\frac { r }{ 100 }  \right)  }^{ 2 }\left[ { \left( 1+\frac { r }{ 100 }  \right)  }-1 \right] =752.64$$
$$\Rightarrow 6272\left[ \frac { r }{ 100 }  \right] =752.64$$
 $$\Rightarrow 6272r=75264$$
 $$r=\frac { 75264 }{ 6272 } =12%$$
Let the sum be P
AS PER PROBLEM, $$6272=P{ \left( 1+\frac { 12 }{ 100 }  \right)  }^{ 2 }$$
       $$6272=P1.2544$$
$$P=\frac { 6272 }{ 1.2544 } =5000$$
Sum of money is 5000 and rate of interest is 12 percent.

Mathematics

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