Question

A sum of money becomes 6 times in 20 years
at a certain rate of interest. Find the
rate of interest ?​

Answer 1

Given:

A sum of money becomes 6 times in 20 years at a certain rate of interest.

To find:

The rate of interest

Solution:

We know,

$\boxed{\bold{Simple\:Interest = \frac{P \times R \times T}{100} }}\\\\\boxed{\bold{Amount = P + S.I. }}$

Let,

"P" → the sum of money

"R" → the rate of interest

"T" → the no. of years

"A" → the amount

The sum becomes 6 times after 20 years

∴ A = 6P . . . . [Equation 1]

Now, by combining both the formulas, we get

$A - P = \frac{P \times R \times T}{100}$

from equation 1, we get

$\implies 6P - P = \frac{P \times R \times T}{100}$

$\implies 5P = \frac{P \times R \times T}{100}$

$\implies 5 = \frac{ R \times T}{100}$

on substituting T = 20 years, we get

$\implies 5 = \frac{ R \times 20}{100}$

$\implies 5 = \frac{ R \times 2}{10}$

$\implies 5 = \frac{ R \times 1}{5}$

$\implies \bold{R = 25\%}$

Thus, the rate of interest is → 25% p.a.

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