Question

At what rate percent simple interest will a sum of money amount to 5/4 of itself in 2 years?
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Answer 1

At 12.5% simple interest the sum of money will amount to 5/4 of itself in 2 years.

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Let's understand a few concepts:

To calculate the simple interest we will use the following formula:

$\boxed{\bold{Simple\:Interest = \frac{Principal \times Rate \times Time}{100} }}$

To calculate the amount in a simple interest we will use the following formula:

$\boxed{\bold{Amount = Principal + S.I.}}$

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Let's solve the given problem:

Let,

"P" → represents the sum of money (Principal)

"R" → represents the rate of simple interest

∴ The amount will be = 5/4 of principal = $\frac{5}{4} P$

The no. of years (T) = 2 years

By combining both the formula above, we can form an equation as,

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

$\implies \frac{5}{4} P - P = \frac{P \times R \times 2}{100}$

$\implies (\frac{5 - 4}{4} )P = \frac{P \times R \times 2}{100}$

$\implies (\frac{1}{4} )P = \frac{P \times R \times 2}{100}$

$\implies (\frac{1}{4} )P = \frac{P \times R }{50}$

$\implies \frac{1}{4} = \frac{ R }{50}$

$\implies R = \frac{50}{4}$

$\implies R = \frac{25}{2}$

$\implies \bold{R = 12.5\%}$

Thus, at 12.5% simple interest the sum of money will amount to 5/4 of itself in 2 years.

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