If a certain sum lent under compound interest becomes 8 times itself in 27 years

Correct Answer - Option 1 : (10/3)%

Given:

Principal becomes 6/5 of itself in 6 years.

Concepts used:

S.I. (Simple interest) = (P × R × T)/100

P → Principal,

R → Rate of interest per annum,

T → Time (in years)

Amount = Principal + S.I.

Calculation:

Let the sum of money lent (Principal) be Rs. x.

S.I. (Simple interest) = (P × R × T)/100

⇒ S.I. = x × R × 6/100

⇒ 6xR/100

Amount = Principal + S.I.

⇒  6/5 of x = x + (6xR/100)

⇒ (6/5)x – x = 6xR/100

⇒ x/5 = 6xR/100

⇒ R = 100/(5 × 6) % p.a.

⇒ R = (10/3) %

∴ The rate of interest earned is (10/3) % p.a.

Let principal = X, A = 3X, T = 8 years, R = ?

Case I,
`"A" = "P"[ 1 + "R"/100 ]^"T"`

`"3X" = "X"[ 1+ "R"/100 ]^8`

`3^(1/8) = 1 + "R"/100 `                ...(1)

Case II,
P = X, A = 27X, T = ?
`27"X" = "X"[ 1 + "R"/100 ]^"T"`

`27^(1/T) = 1 + "R"/100`             ...(2)

From (1) and (2)
`3^(1/8) = 27^(1/T)`

`3^(1/8) = 3^(1/8) = 3/"T"`

T = 24

Time = 24 years.

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A certain sum becomes 3 times ...

Updated On: 27-06-2022

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Answer : B

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