Question

what rate of compound interest will a sum of money become 125/64 of itself in 3 years

Answer 1

In order to make the amount as 125/64 of the sum of money in 3 years, the rate of compound interest will be 25%.

Step-by-step explanation:

Let the sum of money be denoted as “P”, then the amount will become “(125/64)*P”.

Time period, n = 3 years

Also, let the rate of interest be denoted as “R”%

The required formula for calculating the amount in compound interest is,

A = P [1 + R/100]ⁿ

Now, by substituting the values in the formula, we get

$\frac{125}{64} P = P [1 + \frac{R}{100} ]^3$

⇒ $\frac{125}{64} = [1 + \frac{R}{100} ]^3$

Taking cube roots on both sides

⇒ $\frac{5}{4} = 1 + \frac{R}{100}$

⇒ $\frac{R}{100} = \frac{5}{4} - 1$

⇒ $\frac{R}{100} = \frac{5-4}{4}$

⇒ R = ¼ * 100

⇒ R = 25%

Thus, the rate of compound interest is 25%.

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