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Question: The sum of money doubles itself in5 years .find the percent per anum

Posted by: Shrigesh on 29.10.2020

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Left principal = x Then Amount= 2x So interest = 2 x -x =x We know that rate = int ×100/principle × time Rate= x *100/x * 5 Rate = 100/5 Rate =20%per annum

Since, A = 2P, SI = A - P = 2P - P = P.

Now, T = 5 yrs, R = ? 

ATP, P = P.R.5/100 .  => R = 100/5 % = 20 % .p.a.

So, the reqd. rate of interest per annum is 20 % .    (Ans.)


Let the sum of money, Principal be x

Amount after 5 years = 2x

Interest = 2x-x = x

Assuming Simple Interest:

I = PRT/100 (Where I is Interest , P is principal , R is rate of interest , T is time)

So R =  100*I/ PT = 100*x/(x*5)= 20%

Let the sum of money that's principle be x Time=5 yrs Amount after 5 yrs become double =2x therefore s.i=2x-x=x Rate per annum =s.ix100/pxT =x x100/x x 5=20%
Let money be Rs 100 it doubles 200 in time 5 years so it is calculated in simple interest then simple interest is Rs 100 Then by using formula S I =p×r×t/100 ~ 100=100×r×5/100 after calculating we find that rate is 20% ans..

Let the sum of money that's principal be x. Time = 5 years Amount after 5 years becomes double = 2x Therefor, Simple Interest = Amount - Principal = 2x-x = x Rate per annum = SI×100/ P×T = x×100/(x×5) = 100/5 = 20 % 

Here, P=100, A=200, T=5years, S.I. = 100, then, P*R*T/100 , and the rate will be 20%
Let the principal is 100. It doubled. This means Amount ( P + S.I) = 100x2 =200 . Hence Total S I = 200-100=100 in 5 years. Therefore in 1 yr Interest is 100÷5= 20. ie when the principal is 100, Interest is 20 per year. Hence Rate of Inerest = 20% per annum.

S.I = PXRXT/100 so by this fomula rate comes out 20 %


Since the sum of money doubles in 5 years and if you want to know about the rate of interest on this amount  you can calculate both the simple interest and the compound interest.  When calculating simple interest where we get just the extra amount that has to be added to the sum of money (principal) we just write the formula of simple interest I.e., Simple Interest=(principal * rate of interest * Time)/100 here time =5, since the amount of money doubles in 5years here simple interest  = principal because when you add " simple interest"  with the "amount of money " you get 2*amount of money. If you calculate this formula you ll get rate of interest I.e., R = 20% In case of compound interest if compounded (added) annually/quarterly/half yearly where we add the simple interest to the amount every year/4months/6months respectively we get a different rate of interest for different compounding...the formula is A=P{1+(r/n)}^n*t. Where r-rate of interest n- is the compounding frequency(monthly/annually/half yearly/yearly) t-overall time period 






Let the final amount be 2x. Initial amount = x. Therefore the percentage is 2x/x * 100 = 200 percect.




We shall consider both simple interest and compound interest for calculation of interest rates.

i) Simple interest: The formula for simple interest is I= P*T*R/ 100 ,where  P is the principal,

   T =Time period in years and R= rate of interest per year per 100.The principal will double

   if the interest, I, accrued equals the principal P.

   Here Principal= P, Time ,T= 5 years and rate of interest per year per 100 = R

   Therefore  P= P*T*R/100=  P*5*R/100;  that is P= PR/20; which gives R= 20%

ii) Compound Interest: Here we consider that interest is compounded every year The formula for total amount (inclusive of interest) ,A=  P{1+(R/100)}^T. When the principal doubles in 5 years ,the amount

A becomes 2P. Therefore   2P= P{1+(R/100)}^5 ;  which gives {1+(R/100)}^5  = 2

That is { 1+(R/100)}  =  2^(1/5)= 1.1487 or  R= 1.1487 -1 = 0.1487 or 14.87%

Answer: i) Simple  interest R  = 20%  ii) Compound interest R= 14.87%.     

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