Question

the simple interest and compound interest of a sum of money in 2 years are Rs 1000 and 1050 . find the annual rate of interest and principal​

Answer 1

Principal = Rs. 5000

Interest Rate = 10%

Explanation:

• Simple Interest Formula is
  SI = P x n x r/100
  where P = principal, n = number of years and r = interest rate in %

• We have SI = 1000, n= 2 with r and P to be determined

• The simple interest for 2 years = 1000
  Since simple interest is calculated on the principal and remains the same each year,
  First year interest = 1000/2 = 500
  Second year interest = 1000/2 = 500
  
  

• Compound Interest Formula:
  CI = P(1+r/100) - P

• Compound interest is computed on the principal plus interest each year

• First year compound interest is calculated on the Principal = 500
• The interest for the next year = 1050 - 500 = 550

• The additional Rs. 50 comes from the interest calculated on the first year's interest of 500

• Therefore rate of interest = 50/500 = .10 = 10%

Computation of P and r

• Since simple interest for 2 years is P x n x r/100 we have
  1000 = P x 2 x 10/100 = 0.2P

• Therefore principal P = 1000/0.2 = Rs. 5000
  

• Answer: Principal is Rs. 5000 and interest rate is 10%

• Cross-check
• Principal of 1000 and interest rate of 10% for 2 years gives:
  SI = 5000 x 2 x 10/100 = 1000
  

• CI = 5000(1 + 10/100)² - 5000
  =5000(1.1)² - 5000
  = 5000(1.21) - 5000
  = 6050 - 5000 = 1050
  
  

So calculations check out