C.I. on a sum is 320 in 2nd year & 2000 in 4th year. C.I. in the 3rd year ?
Answers
Answer:
Step-by-step explanation:
Answer:
Rs 800
Step-by-step explanation:
Let say Principal = P
Let say interest Rate = 100R % per annum
Interest in 1st Year = P100R/100 = Rs PR
Interest in two years = P( 1 + 100R/100)² - P
Interest in second Year = Interest in two years - interest in 1st Year
P( 1 + R)² - P - PR = 320
=> P ( 1 + R² + 2R - 1 - R) = 320
=> P (R² + R) = 320
=> PR(R + 1) = 320 - eq 1
Interest in 4 years = P( 1 + R)⁴ - P
Interest in 3 years = P( 1 + R)³ - P
interest in 4th year = P( 1 + R)⁴ - P( 1 + R)³
P( 1 + R)⁴ - P( 1 + R)³ = 2000
=> P( 1 + R)³ ( 1 + R - 1) = 2000
=> P( 1 + R)³ (R) = 2000 eq2
eq 2/ eq1
(1 + R)² = 2000/320
=> ( 1 + R)² = 100/16
=> ( 1 + R)² = 10/4
=> 1 + R = 2.5
=> R = 1.5
interest Rate = 100R = 150 % per annum
P(1.5)(1.5 + 1) = 320
=> P = 256/3
compound interest in 3rd year = P( 1 + R)³ - P( 1 + R)²
= PR(1 + R)²
=PR(1+R)(1+R)
= 320(1 + R)
= 320(1 + 1.5)
= 320(2.5)
= 800
Amount Rate Interest
85.33333333 150% 128
213.3333333 150% 320
533.3333333 150% 800
1333.333333 150% 2000