An amount of money appreciates to ₹ 7,000 after 4 years

An amount of money appreciates to ₹ 7,000 after 4 years and to ₹ 10,000 after 8 years at a certain compound interest compounded annually. The initial amount of money was

Here , A₁ = ₹ 7,000 , T₁ = 4 years and A₂ = ₹ 10,000 , T₂ = 8 years
Using the given formula ,

A = P		1 +	R		^T
			100

⇒ 7000 = P		1 +	R		⁴	..... (i)
			100

10000 = P		1 +	R		⁸	..... (ii)
			100

Dividing equation (ii) by (i)

10000	=		1 +	R		⁴
7000				100

⇒	10	=		1 +	R		⁴
	7				100

From equation (i),

7000 = P ×	10
	7

⇒ P = ₹ 4900
We can find required answer with the help of given formula :
Here, b – a = 8 – 4 = 4 and B = Rs 10,000 , A = Rs,7000

R% =			B		^1/n	− 1		× 100%
			A

R% =			10000		^1/4	− 1
			7000

R% =			10		^1/4	− 1
			7

⇒ 1 +	R	=		10		^1/4
	100			7

⇒		1 +	R		⁴	=	10
			100				7

Using ,

∵ Amount = P		1 +	R		⁴
			100

⇒ 7000 = P ×	10
	7

∴ P = Rs. 4900