Question

A sum of money becomes 256/81 times of itself in 4 years compounded annually . Find rate of interest.
pls anyone tell ​

Answer 1

Question :- A sum of money becomes 256/81 times of itself in 4 years compounded annually . Find rate of interest. ?

Solution :-

Let us assume that, the given sum of money is Rs.81x .

So,

→ Principal = Rs.81x

→ Rate = Let R% per annum compounded annually .

→ Time = 4 years.

→ Amount = (256/81) times of Principal = (256/81) * 81x = Rs.256x

we know that, when rate is compounded annually,

• Amount = Principal * [ 1 + (Rate/100) ]^(Time)

Putting all values we get :-

→ 256x = 81x * [ 1 + (R/100) ]⁴

→ (256x/81x) = [ 1 + (R/100) ]⁴

→ (256/81) = [ 1 + (R/100) ]⁴

→ (4⁴/3⁴) = [ 1 + (R/100) ]⁴

→ (4/3)⁴ = [ 1 + (R/100) ]⁴

Now we know that, if m = n in a^m = b^n . than, a = b .

Therefore,

→ (4/3) = [ 1 + (R/100) ]

→ (4/3) - 1 = (R/100)

→ (1/3) = (R/100)

→ R = (100/3)

→ R = 33.33% .(Ans.)

Hence, Required rate of interest will be 33.33% .

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