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:
Answer & explanation
Correct answer: option 2
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