A sum of ₹ 12,000, deposited at compound interest becomes

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A sum of ₹ 12,000, deposited at compound interest becomes double after 5 years. How much will it be after 20 years ?

1. ₹ 1,44,000
2. ₹ 1,20,000
3. ₹ 1,50,000
4. ₹ 1,92,000

Correct Option: D

Here , Principal ( P ) = ₹ 12,000 , Amount = 2P = ₹ 24,000 , Time = 5 years , Rate = R%

A = P		1 +	R		^T
			100

⇒ 24000 = 12000		1 +	R		⁵
			100

⇒ 2 =		1 +	R		⁵
			100

Now, we have 2⁴ =		1 +	R		²⁰
			100

∴ The sum amounts to 16 times of principal i.e. ₹ 192000 after 20 years.
Second Method to solve this question :
Here, p = 2, n₁ = 5
q = ?, n₂ = 20
∴ p^1/n₁ = q^1/n
2^1/5 = y^1/20
⇒ y = (2^1/5)^{²⁰
q = 2⁴
q = 16 times
∴ Sum = 16 × 12000 = ₹ 1,92,000}