The compound interest amounts on a certain sum at a certain rate percentagep.a. for the second year andthird year are ₹3,300 and ₹3,630, respectively. What is the amountof the same sum atthe samerate in $$2\frac{1}{2}$$ years, interest compounded yearly?

Compound interest after 2nd and 3rd year = Rs. 3300 and Rs. 3630 respetively.

Thus, difference between compound interest for 3rd year = $$3630-3300=Rs.$$ $$330$$

Thus, rate of interest = $$\frac{330}{3300}\times100=10\%$$

Let principal sum = Rs. $$P$$

Thus, C.I. for 2nd year = $$P[(1+\frac{r}{100})^2-1]-P[(1+\frac{r}{100})-1]$$

=> $$P[(1+\frac{10}{100})^2-1]-P[(1+\frac{10}{100})-1]=3300$$

=> $$P[(1.1)^2-1]-P[0.1]=3300$$

=> $$P=\frac{3300}{0.11}=Rs.$$ $$30,000$$

$$\therefore$$ Amount after $$2\frac{1}{2}$$ years = $$P\times(1+\frac{10}{100})^2\times(1+\frac{10}{2\times100})$$

= $$30,000\times(\frac{121}{100})\times(\frac{21}{20})$$

= $$15\times121\times21=Rs.$$ $$38,115$$

=> Ans - (C)