The compound interest on a certain sum at $$16\frac{2}{3}\%$$ p.a. for 3 years is ₹6,350. What will be the simple interest on the same sum at the samerate for $$5\frac{2}{3}$$ years?

Compound interest = 6350

Rate(r) = $$16\frac{2}{3}\%$$ = (50/3)%

Time(t) = 3 years

Compound interest = p(1 + $$\frac{r}{100})^t - p$$

6350 = p(1 + $$\frac{50/3}{100})^3 - p$$

6350 = p(1 + $$\frac{1}{6})^3 - p$$

6350 = p $$\times \frac{7}{6} \times \frac{7}{6} \times \frac{7}{6}- p$$

6350 = 1.588p - p

0.588p = 6350

p = 6350/0.588 = 10800

Simple interest = $$\frac{prt}{100}$$

r = (50/3)%

t = $$5\frac{2}{3}$$ = 17/3

Simple interest = $$\frac{10800 \times (50/3) \times (17/3)}{100}$$ = Rs.10200