Question

the simple interest and the compound interest of a capital are respectively by rs 1440 and 1483.20 in 2 yrs. determine the rate of interest.

Answer 1

Answer:

the rate of interest = 6 % per annum

Step-by-step explanation:

Simple interest  = P * R * T /100  = 2PR/100

=> 2PR/100 = 1440

=> PR = 72000

=> P = 72000/R

Compound interest = P(1 + R/100)^T  - P

= P (1 + R/100)² - P

= P ((1 + R/100)² - 1)

P ((1 + R/100)² - 1)  = 1483.20

=> (72000/R )((1 + R/100)² - 1)  = 1483.20

=> 72000 ( 1  + R²/10000 + 2R/100 - 1)  = 1483.2 R

=> 7.2R² + 1440R = 1483.2 R

=> 7.2R² = 43.2R

=> 7.2R  =43.2

=> R = 6

the rate of interest = 6 % per annum

Another Way to solve

Simple interest for 2 years = 1440

Simple interest for 1 Year = 1440/2 = 720

Difference in compind interest & simple interest fro 2 years = 1483.2 - 1440

= 43.2 Rs

this difference is because of interest on 1st Year interset

=> 43.2 = 720 * R * 1/100

=> R = 4320/720

=> R = 6