In what time will a sum of money doubles itself at 10 pa compound interest payable half yearly?

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In how many years will a sum of money double itself at 10% per annum simple interest?
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In what time will a sum of money double itself at 10 pa compound interest payable half yearly?
At what rate of simple interest will a sum of money double itself in 10 year?
How many years will it take for a sum of money to double at 10% compounded annually?
In what time will a sum of money double itself at 5% compound interest payable half yearly?

Bihar Police SI Prelims 2020: Full Mock Test

100 Questions 200 Marks 120 Mins

Let, the sum be Rs x and Rate of interest be r%

According to the question,

2x = x (1 + r/100)15

⇒ (1 + r/100)15 = 2 ----(i)

Now, Required amount = 8x

Let time period be ‘t’ years

8x = x(1 + r/100)t

⇒ (1 + r/100)t = 8 = 23

⇒ (1 + r/100)t = [(1 + r/100)15]3 [from (i)]

⇒ (1 + r/100)t = (1 + r/100)45

⇒ t = 45

∴ In 45 years, it will become 8 times.

Latest Bihar Police SI Updates

Last updated on Sep 22, 2022

Bihar Police Subordinate Service Commission (BPSSC) has activated the link to download the mark sheet of Bihar Police Sub Inspector on 21st August 2022. The candidates, who appeared for Bihar Police SI exam, must check their results before 4th September 2022.The new notification for 2022-23 cycle is expected to be released soon.

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In how many years will a sum of money double itself at 10% per annum simple interest?

4 years
8 years
10 years
6 years

Answer (Detailed Solution Below)

Option 3 : 10 years

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Bihar Police Fireman Full Mock Test 2021

100 Questions 100 Marks 120 Mins

Given:

the sum of money doubles itself.

Rate = 10%

Concept used:

S.I. = PRT/100

Amount = P + SI

Calculation:

Amount = 2P = P + P

Let the Principal be 100, then Simple Interest = 100

⇒ 100 = (100 × 10 × T)/100

⇒ T = 10 years

∴ Time taken is 10 years.

Latest Bihar Police Fireman Updates

Last updated on Sep 26, 2022

Bihar Police Fire Admit Card released for the Physical Efficiency Test. The Central Selection Board of Constables (CSBC) will conduct the PET on 8th November 2022. Earlier, the Bihar Police Fireman Result for the written examination was released on 5th September 2022. Candidates who had qualified the same are only eligible for the PET. The candidates shortlisted for the post of Bihar Police Fireman will get a salary range between Rs. 21,700 to Rs. 69,100.

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Answer

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Hint: To solve the problem, we should know the definition of annual simple interest. We have,
Simple Interest (I) = $\dfrac{P\times R\times t}{100}$
Where, P= principal amount
R = simple interest annual rate
t = time period of the annual simple interest
Here, we have R = 10% and have to calculate t for the sum of the money (that is P) to double.

Complete step-by-step answer:
In this question, we are left with two unknowns, P and t. However, we also have an additional condition. This condition tells that within the required time (which we have to calculate), the sum of money doubles itself. Thus, if originally, we had principal amount as P, finally, this amount would become 2P. Thus, simple interest (I) becomes 2P-P = P. Since, simple interest is basically the amount accumulated over the total principal amount. Further, for simplification, we can write,
$\dfrac{R}{100}=\dfrac{10}{100}=0.1$
Thus, we have,
I=$\dfrac{P\times R\times t}{100}$
Since, I = P (as calculated above), we have,
P = $\dfrac{P\times R\times t}{100}$
We can cancel P from both sides. Thus, we have,
1=$\dfrac{R\times t}{100}$
Plugging in the known values, we have,
1= 0.1$\times $t
Since, $\dfrac{R}{100}$=0.1
Now,
t=10 years
Hence, it will take 10 years for the sum of money to double itself with the rate of 10% per annum simple interest.

Note: While solving questions related to principal interest, it is important to keep in mind that simple interest calculated from the formula, Simple Interest (I) = $\dfrac{P\times R\times t}{100}$ , doesn’t represent the total amount of money. In fact, the total amount is the sum of Principal amount (P) and simple interest. Thus, in this case, when money was doubled, the total amount was 2P and simple interest was P.

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Watch More Solved Questions in Chapter 7

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Problem 7

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Problem 12

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Problem 15

Problem 16

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Dr. J K Das
Business Mathematics and Statistics

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In what time will a sum of money double itself at 10 pa compound interest payable half yearly?

∴ Time taken is 10 years. The Central Selection Board of Constables (CSBC) will conduct the PET on 8th November 2022.

At what rate of simple interest will a sum of money double itself in 10 year?

As we know the simple interest means principle amount subtracted from final amount i.e. Hence the required rate in which the sum becomes double itself in 10 years is 10%.

How many years will it take for a sum of money to double at 10% compounded annually?

To find out how long it would take a sum to double, divide 72 by the rate. As such, at 10% interest, your sum will double in 7.2 years.

In what time will a sum of money double itself at 5% compound interest payable half yearly?

This is an Expert-Verified Answer Here we need to double the money so the amount becomes 2P. Therefore, the number of years it will take to double the money at 5% per annum when compounded annually is 12.5 years.