1.

If the difference between the compound interest and simple interest at 17% on a sum of money for 2 years (compounded annually) is Rs. 433.50, then the sum (in Rs.) is:1. 12,0002. 20,0003. 15,0004. 25,000

Answer» Correct Answer - Option 3 : 15,000

Given:

Rate of interest = 17%

Time = 2 years

The difference between CI and SI = Rs. 433.50

Formula used:

Simple interest = P × R% × T

Calculation:

Let the principal be Rs. x.

SI = P × R% × T

⇒ SI = x × 17% × 2

⇒ SI = x × 17/100 × 2

⇒ SI = 34x/100

⇒ SI = 0.34x

In the case of CI:

1st year CI = P × R% × T

⇒ 1st year CI = x × 17% × 1

⇒ 1st year CI = 17x/100

⇒ 1st year CI = 0.17x

Amount after 1st year = P + CI 

⇒ Amount = x + 0.17x

⇒ Amount = 1.17x

2nd year CI = 1.17x × 17% × 1

⇒ 2nd year CI = 0.1989x

Total CI = 1st year CI + 2nd year CI

⇒ CI = 0.17x + 0.1989x

⇒ CI = 0.3689x

Required difference = CI – SI

⇒ 433.50 = 0.3689x – 0.34x

⇒ 433.50 = 0.0289x

⇒ x = 433.50/0.0289

⇒ x = Rs. 15000

∴ The sum is Rs. 15000.



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