A sum becomes ₹ 4500 after two years and ₹ 6750 after

A sum becomes ₹ 4500 after two years and ₹ 6750 after four years at compound interest. The sum is

Given in question , A₁ = ₹ 4500 , T₁ = 2 years and A₂ = ₹ 6750 , T₂ = 4 years
Suppose principal = P

P		1 +	r		²	= 4500 ..... (i)
			100

P		1 +	r		⁴	= 6750 ..... (ii)
			100

On dividing equation (ii) by equation (i), we get

	1 +	r		²	=	6750
		100				4500

From equation (i), we get

P ×	6750	= 4500
	4500

⇒ P =	4500 × 4500	= ₹ 3,000
	6750

Second Method to solve this question :
Here, b – a = 4 – 2 = 2 and B = ₹ 6750, A = ₹ 4500

R% =			B		^1/2	− 1		× 100%
			A

R% =			6750		^1/2	− 1		× 100%
			4500

R% =			3		^1/2	− 1		× 100%
			2

⇒		3		^1/2	= 1 +	R
		2				100

⇒	3	=		1 +	R		²
	2				100

Using formula ,

A = P		1 +	R		²
			100

4500 = P ×	3
	2

P = ₹ 3000