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:

₹18,000

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.