At what rate percent per annum will a sum of money double itself in 8 years 4 months?

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Answer (Detailed Solution Below)
The correct option is A12.5%Explanation for the correct option:Consider that sum is invested under simple interest.The formula for the simple interest SI is given as SI=P×R× N100Where , P is the principal amount, R is the percentage rate of interest per annum,N is the number of years for which the sum is invested.The amountA is given as A=P+SIAccording to given condition it is known that the amount is doubled.⇒A=2P⇒2P =P+SI⇒SI=PSubstituting the values in the formula of simple interest we get⇒P=P× R×8100⇒R=1008⇒R=12.5%Thus the given amount will double in 8 years at 12.5%per annum.Hence, option(A) i.e. 12.5% is the correct answer.
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Answer (Detailed Solution Below)

Option 1 : 20%

Formula for Simple Interest -

\(SI = \frac{{P \times R \times T}}{{100}}\)

Where,

P = Principal

R = Rate of interest

T = Time period

Let the required rate of interest be X.

According to the question, SI must be equal to 2 × P in order to make the final sum two times the original principal amount after 5 year.

\(\therefore {\rm{P}} = {\rm{}}\frac{{{\rm{P}} \times {\rm{X}} \times 5}}{{100}}\)

⇒ X = 20%

∴ Required rate of interest is of 20%.

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Solution

The correct option is A12.5%Explanation for the correct option:Consider that sum is invested under simple interest.The formula for the simple interest SI is given as SI=P×R× N100Where , P is the principal amount, R is the percentage rate of interest per annum,N is the number of years for which the sum is invested.The amountA is given as A=P+SIAccording to given condition it is known that the amount is doubled.⇒A=2P⇒2P =P+SI⇒SI=PSubstituting the values in the formula of simple interest we get⇒P=P× R×8100⇒R=1008⇒R=12.5%Thus the given amount will double in 8 years at 12.5%per annum.Hence, option(A) i.e. 12.5% is the correct answer.

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At what rate a sum doubles its...

Updated On: 27-06-2022

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