The ratio of difference between compounded interest and simple interest for 3years to the difference between C.I and S.I for 2years is 31 : 10. What is rate of percent per annum ?
Answers
Answer:
Let P is the initial amount of money,
r is the rate of interest per annum
T is the time,
Then, compound interest for 3 years = P(1 + r/100)³ - P
simple interest for 3 years = P × r × 3/100
then, CI - SI = P(1 + r/100)³ - P - 3Pr/100
= P[1 + r³/100³ + 3r²/100² + 3r/100 - 1 - 3r/100]
= P[ r³/100³ + 3r²/100² ]
= P(r/100)²[r/100 + 3]
again,
Compound interest for 2 years = P[ (1 + r/100)² - 1]
simple interest for 2 years = P × r × 2/100
C.I - S.I = P[1 + r²/100² + 2r/100 - 1 - 2r/100]
= P(r/100)²
Now, A/C to question,
{(CI-SI) for 3 years }/{(CI - SI) for 2 years} = 23/7
P(r/100)² [r/100 + 3]/P(r/100)² = 23/7
⇒r/100 + 3 = 23/7
⇒ r/100 = 23/7 - 3 = 2/7
r = 200/7 %
Hence, answer is 200/7 %
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Sorry its my question also
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