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?

Principal = p

Rate(r) = 10%

Time(t) = 1 year

compound interest = $$p(1 + r/100)^t - P$$

When interest is calculated yearly = $$p(1+ 10/100) - p = p \times (110/100) - p$$

When interest is calculated half yearly,

Rate(r) = 10/2 = 5%

Time(t) = 1 $$\times$$ 2 = 2

Interest = $$p(1 + 5/100)^2 - p = p \times (105/100) \times (105/100) - p 

Difference of interest = 88.80

$$p \times (105/100) \times (105/100) - p - p \times (110/100) + p = 88.80$$

$$p \times 1.05 \times 105 - p \times 110 = 8880$$

110.25p - 110p = 8880

p = 8880/.25 = 35520

Simple interest for $$1\frac{2}{3}$$ years,

t = $$1\frac{2}{3}$$ = 5/3 years

Interest = $$\frac{prt}{100} = \frac{35520 \times 10 \times 5}{100 \times 3}

= Rs.5920