The simple interest on a certain sum of money for 5 years at the rate of 10% per annum is half the compound interest on ₹5,000 for 2 years at the rate of 10% per annum, interest compounded yearly. The sum placed on simple interest is:

₹1,050

The formula that we used here is :-

Amount = P$(1 \;+\; \frac{R}{100})^t$

Compound interest = Amount - Principal

= [ 5000 × ( 1 +  \(\frac{10}{100}\) )² ] - 5000

= [ 5000 × \(\frac{11}{10}\)  × \(\frac{11}{10}\) ] - 5000

= 6050 - 5000

= 1050

ATQ,

SI is half of CI = \(\frac{1050}{2}\) = Rs.525

Now,

Simple Interest = \(\frac{P × R × T}{100}\)

525 = \(\frac{P × 5 × 10}{100}\)

525 = \(\frac{5P}{10}\)

P = Rs.1050