The difference in compound interest on a certain sum at 10% p.a. for one year, when the interest is compounded half yearly and yearly, is ₹88.80. What is the simple interest on the same sum for $1\frac{2}{3}$ years at the same rate?

₹5,920

Rate of compound interest for 1 year ( compounded annually ) = 10%

Rate of compound interest for 6 months ( compounded half yearly )  = 5%

Net interest rate when interest in compounded half yearly = 5 + 5 + \(\frac{ 5 × 5 }{100}\)
= 10.25%

ATQ,

Required difference = 10.25% - 10% = 0.25%

0.25% = 88.80

1% = 355.2

 Sum = 100% = 100 × 355.2 = Rs. 35520

Now,

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

= \(\frac{35520 × 10 × 5  }{3 ×100}\)

= \(\frac{35520   }{3 × 2}\)

= Rs.  5920