Question

Hii brainly wasio,

If a sum of money doubles itself at the fixed rate of compound interest per annum in n years, let us write in how many years will it become four times.

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Answer 1

Answer:

Let A = amount, P = principal, r = rate of interest compounded per annum and n = number of years.

Let it be in ‘n’ years A in compound interest will amount to 2A.

∴ Amount for n years = A (1 + r)n

By the condition, A (1 + r)n = 2A

⇒ (1 + r)n = 2A/ A

⇒ (1 + r)n = 2

⇒ (1 + r) = 21/n … (1)

Let the amount become 4 times in t years.

⇒ 4A = A(1 + r)t

⇒ (1 + r)t = 4

⇒ (1 + r)t = 22

⇒ (1 + r) = 22/t… (2)

From (1) and (2),

⇒ 21/n = 22/t

∴ t = 2n

∴ The sum of money will become four times in 2n years.

Step-by-step explanation:

Answer 2

Let A = amount, P = principal, r = rate of interest compounded per annum and n = number of years.

Let it be in ‘n’ years A in compound interest will amount to 2A.

∴ Amount for n years = A (1 + r)n

By the condition, A (1 + r)n = 2A

⇒ (1 + r)n = 2A/ A

⇒ (1 + r)n = 2

⇒ (1 + r) = 21/n … (1)

Let the amount become 4 times in t years.

⇒ 4A = A(1 + r)t

⇒ (1 + r)t = 4

⇒ (1 + r)t = 22

⇒ (1 + r) = 22/t… (2)

From (1) and (2),

⇒ 21/n = 22/t

∴ t = 2n

∴ The sum of money will become four times in 2n years.