Question

12,000 is invested for 1.5
years at C.I. If 15,972 is received at the end of this period,find the rate of interest per annum.​

Answer 1

Answer:R = 21 %

R = 20.64 %

Step-by-step explanation:

Let say rate of interest = R

Interest for 1st Year = 12000 * R * 1 /100  = 120 R

Amount after 1 years = 12000 + 120R  

interest for next 1/2 years =  (12000 + 120R) * (1/2) R /100

= (120 + 1.2R)R/2

= 60R + 0.6R²

120 R  + 60R + 0.6R²  = 15972 - 12000

=> 0.6R² + 180R = 3972

=> R² + 300R  = 6620

=> R² + 300R  - 6620 = 0

=> R = 20.64 %

But  if We calculate

Amount = P (1 + R/100)ⁿ

=> 15972 = 12000 ( 1 + R/100)^(3/2)

=> 1.331 =  ( 1 + R/100)^(3/2)

=> 1.1 = √(1 + R/100)

=> 1.21 = 1 + R/100

=> R/100 = 0.21

=> R = 21 %

Answer 2

Answer:

R = 21 %

R = 20.64 %

Step-by-step explanation:

Let say rate of interest = R

Interest for 1st Year = 12000 * R * 1 /100 = 120 R

Amount after 1 years = 12000 + 120R

interest for next 1/2 years = (12000 + 120R) * (1/2) R /100

= (120 + 1.2R)R/2

= 60R + 0.6R²

120 R + 60R + 0.6R² = 15972 - 12000

=> 0.6R² + 180R = 3972

=> R² + 300R = 6620

=> R² + 300R - 6620 = 0

=> R = 20.64 %

But if We calculate

Amount = P (1 + R/100)ⁿ

=> 15972 = 12000 ( 1 + R/100)^(3/2)

=> 1.331 = ( 1 + R/100)^(3/2)

=> 1.1 = √(1 + R/100)

=> 1.21 = 1 + R/100

=> R/100 = 0.21

=> R = 21 %