Mr.P.K. Dubey invested certain sum on simple interest and the same sum on compound interest at a certain rate on
interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25: 8. The rate of interest per annum is?
Answers
Given : invested certain sum on simple interest and the same sum on compound interest at a certain rate on interest per annum . ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25: 8
To find : rate of interest per annum
Solution:
Let say Amount = P
rate of interest = R
SI for 2Years = P * R * 2 /100 = 2PR/100
CI for 2 Year = P(1 + R/100)² - P
Difference in CI & SI = P(1 + R/100)² - P - 2PR/100
= P ( 1 + R²/100² + 2R/100 - 1 - 2R/100)
= P R²/100²
SI for 3 Years = P * R * 3 /100 = 3PR/100
CI for 3 Year = P(1 + R/100)³ - P
Difference in CI & SI = P(1 + R/100)³ - P - 3PR/100
= P ( 1 + R³/100³ + 3R/100 + 3R²/100² - 1 - 3R/100)
= (P R²/100)( R/100 + 3)
(P R²/100)( R/100 + 3)/ (P R²/100² ) = 25/8
=> 8R/100 + 24 = 25
=> 8R/100 = 1
=> R = 12.5
Rate of interest per annum = 12.5 %
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