Question

In how much time will a sum of money double if invested at the rate of 8% simple interest per annum? ​

Answer 1

• The time will a sum of money double itself if once rated at the rate of 8% simple interest per annum = 12.5 years OR 150 months.

Given :

• A sum of money double itself if invested at the rate of 8%.

To Find :

• The time will a sum of money double itself if once rated at the rate of 8% simple interest per annum.

Solution :

Let,

• Time be T.

• The sum of the money be Rs. x.

According to the question,

The sum of the money double itself.

• The amount be Rs. 2x.

First, we need to find the interest.

$\bf S.I. = \dfrac{S \times T \times R}{100}$

Where,

• S.I. = Simple Interest.
• S = Sum of the money.
• T = Time.
• R = Rate.

$\bf \implies \dfrac{x \times T \times8 }{100} \\ \\ \\ \bf \implies \dfrac{8x \times T}{100}$

Hence, the interest is $\bf\dfrac{8x \times T}{100}$

Now, we have to find the time by using the formula of amount.

$\bf A = S + S.I.$

Where,

• A = Amount.
• S = Sum of the money.
• S.I. = Simple Interest.

$\bf \implies 2x = x + \dfrac{8x \times T}{100} \\ \\ \\ \bf \implies 2x = \dfrac{100x + 8x \times T}{100} \\ \\ \\ \bf \implies 2x \times 100 = 100x + 8x \times T \\ \\ \\ \bf \implies 200x = 100x + 8x \times T \\ \\ \\ \bf \implies 200x - 100x = 8x \times T \\ \\ \\ \bf \implies 100x = 8x \times T \\ \\ \\ \bf \implies \dfrac{100\not{x}}{8\not{x}} = T \\ \\ \\ \bf \implies \dfrac{100}{8} = T \\ \\ \\ \bf \implies 12.5 = T \\ \\ \\ \: \: \therefore \: \bf \: time (T)= 12.5 \: years$

In months :-

For converting years in months, we have to multiple the value by 12.

So we have,

• Time = 12.5 years

$\bf \implies12.5 \times 12 \: \: months \\ \\ \bf \implies 150 \: \: months$

Hence,

The time will a sum of money double itself if once rated at the rate of 8% simple interest per annum is 12.5 years OR 150 months.