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 PAS 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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