If the difference between the compound interest and simple interest on a certain sum of money for three years at 10% p.a. is ₹558, then the sum is:
Answer & explanation
Correct answer: option 2
The formulas that we used here is :-
Simple interest = \(\frac{ P × R × T}{100}\)
Compound interest = P$[(1 \;+\; \frac{R}{100})^t - 1 ]$
According to question,
Difference in compound interest and simple interest,
558 = P$[(1 \;+\; \frac{10}{100})^3 - 1 ]$ - \(\frac{ P × 10 × 3}{100}\)
558 = P[$\frac{331}{1000}$] - \(\frac{ 3P}{10}\)
558 = P[ \(\frac{ 331}{1000}\) - \(\frac{ 3}{10}\) ]
558 = P[ \(\frac{ 331 - 300}{1000}\) ]
558 = P[ \(\frac{ 31}{1000}\) ]
P = 18000
So, Initial sum is Rs. 18000.