# A. THE DIFFERENCE BETWEEN COMPOUND INTEREST AND SIMPLE INTEREST ON A SUM OF RS 3000 FOR 3 YEARS IS RS 93.THE RATE PERCENT PER ANNUM IS?

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by jashnkumar12

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by jashnkumar12

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Principle= P=3000, time =t=3 and rate of interest=r

Then for C I=P(1+r)³-P =3000(1+r)³-3000

For simple interest S I= P*r*t= 3000*3*r

we have 3000(1+r)³-3000- 9000r=93

⇒ 3000+3000r³+9000r²+9000r-3000-9000r=93

⇒ 3000r³+9000r²-93=0

⇒ 3000r³ -300r²+9300r²-93=0

⇒ 300r²(10r-1)+93(100r²-1)=0

⇒ 300r²(10r-1)+93 (10r+1)(10r-1)=0

⇒ (10r-1)(300r²-930r-93)=0

solving we have 10r-1=0 or r=1/10=10%

Hence interest rate is 10%

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P(1+r)³ - P - P r 3 = 93

r³ + 3 r² + 3 r + 1 - 1 - 3 r = 93 /3000

r³ + 3 r² = 0.031

r is a fraction, like 10% or 0.1, so r³ is much smaller than r². Neglect r³ term.

r² ≈ 0.031 /3

r ≈ 0.101653

Let us try r = 0.1 or 10% per annum.

0.1³ + 3 0.1² = 0.031 => r = 10%

You can also use the standard cubic equation solution methods to find answer.

r³ + 3 r² + 3 r + 1 - 1 - 3 r = 93 /3000

r³ + 3 r² = 0.031

r is a fraction, like 10% or 0.1, so r³ is much smaller than r². Neglect r³ term.

r² ≈ 0.031 /3

r ≈ 0.101653

Let us try r = 0.1 or 10% per annum.

0.1³ + 3 0.1² = 0.031 => r = 10%

You can also use the standard cubic equation solution methods to find answer.