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

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

Answer

Verified

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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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.

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Last updated on Sep 22, 2022

Bihar Police Sub-Ordinate 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. For Bihar Police vacancy 2020, the BPSSC had released as many as 1998 vacancies for the post of sub-inspector and 215 vacancies for the post of sergeant. Those who could not make it to the final merit list, should not lose their heart as the notification for 2022 is expected to be out very soon.

Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

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

1. 4 years
2. 8 years
3. 10 years
4. 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

The Central Selection Board of Constables (CSBC) will conduct the PET exam for Bihar Police Fireman on 8th November 2022. The admit card will be available on the official website from 12th October 2022. The Bihar Police Fireman Result for the written examination took place on 5th September 2022. The qualified candidates for the written examination will go for the next round which is the Physical Efficiency Test (PET). The PET round will be conducted in the month of November 2022. The candidates for the post of Bihar Police Fireman will get a salary range between Rs. 21,700 to Rs. 69,100.

Let's discuss the concepts related to Interest and Simple Interest. Explore more from Quantitative Aptitude here. Learn now!

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