Question

A sum of money is put at a compound interest for 2 years at 20% pa. It would fetch 482 more if the interest were payable half yearly than if it were payable yearly. Find the sum.

Answer 1

Answer = 20,000.

Given that :-

• A sum of money is put at a compound interest for 2 years at 20% pa.

• It would fetch 482 more if the interest were payable half yearly

To find :-

• The sum.

$\huge{\sf{\boxed{\boxed{Solution:}}}}$

Let the sum be x.

$x( 1\ + \frac{10}{100} ) {}^{4} - x(1 \ + \frac{20}{100} ) {}^{2} = 482 \\ \\ = x( \frac{11}{10}) {}^{4} - x( \frac{6}{5} ) {}^{2} = 482 \\ \\ = x(1.4641 - 1.44) = 482 \\ \\ = 0.0241x = 482 \\ \\ x = \frac{482}{0.0241} = 20000$

The sum = Rs. 20,000.