The compound interest on a certain sum in $$2\frac{1}{2}$$ years at 10% p.a., interest compounded yearly, is ₹1,623 The sum is:

As per the given question,

Let the sum amount is =P

time (t)=$$2\dfrac{1}{2}$$

Rate of interest (R)= 10% p.a.

Compound interest =1,623 Rs.

Now, we know that $$A=P \left( 1+\dfrac{R}{100} \right)^t$$

So, $$A=P\left(1+\dfrac{10}{100}\right)^2$$

$$\Rightarrow A=P\left(\dfrac{11}{10}\right)^2$$

Compound interest in 2 years $$=P\left(\dfrac{11}{10}\right)^2-P$$

Interest in 1/2 years $$=\dfrac{121P\times R\times t}{100\times100}=\dfrac{121P\times 10\times 1}{100\times 2\times 100}=\dfrac{121P}{2000}$$

Hence, net interest, $$1623=\dfrac{121P}{2000}+P\left(\dfrac{11}{10}\right)^2-P$$

$$\Rightarrow 1623=\dfrac{121P}{2000}+\dfrac{21P}{100}$$

$$\Rightarrow 541P=1623\times 2000$$

$$\Rightarrow P=6000$$Rs.