Question

a sum of money amounts to rs
9360 in 7 years at 8% simple
interest. will it double itself at the
same rate.​

Answer 1

Answer:

Hence, the rate of interest to double a money in 8 years will be 12.5% per annum.

Answer 2

It will double itself in 12.5 years at the same rate of simple interest.

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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 simple interest we will use the following formula:

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

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Let's now solve the given problem:

Finding the sum of money:

Let the sum of money be "P".

The amount = Rs. 9360

The no. of years i.e., Time = 7 years

The rate of interest i.e., Rate = 8% p.a.

By using the above two formulas of simple interest, we get,

$Amount = Principal + \frac{Principal\times Rate \times Time}{100}$

$\implies 9360 = P + \frac{P\times 8 \times 7}{100}$

• on multiplying by 100

$\implies 9360 \times 100 = 100P + 56P$

$\implies 9360 \times 100 =156P$

$\implies P = \frac{9360 \times 100}{156}$

$\implies \bold{P =6000}$ ← sum of money

Finding the no. of years when the sum of money doubles itself:

Here we have,

Amount = $2 \times P = 2 \times 6000 = Rs.\: 12000$

Rate of simple interest = 8% p.a.

Since Amount = P + S.I.

∴ $12000 = 6000 + \frac{6000 \times Time \times 8}{100}$

$\implies 12000 - 6000 = \frac{6000 \times Time \times 8}{100}$

$\implies 6000 = \frac{6000 \times Time \times 8}{100}$

$\implies 6000 = 60 \times Time \times 8$

$\implies 6000 = 480 \times Time$

$\implies Time = \frac{6000}{480}$

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

$\implies \bold{Time =12.5\:years}$

Thus, the sum of money will double itself by 12.5 years at the same rate.

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