Question

A sum of Rs 12,800 earns Rs 2017.60 in 18 months, when the rate of interest is reckoned half yearly. Find the rate.

Answer 1

R  = 12800 (1 + r )^n
this is compound interest situation.  Since r is compounded half yearly. Let us take the interest at half yearly basis.  r is interest per 6 months.  in 18 months, we have half years.  So interest is compoinded 3 times.  so  n = 3
R = 12800 + 2017.60 = principal + interest = Rs  14817.60
So 14817.60 = 12800  (1+r)³              so (1+r)³ =  14817.60 / 12800 
  So 1 + r = 1.05    =>  r = 0.05  =>  r = 5 %
Rate for 6 months is 5% . Rate per annum will be twice that is 10%.

Answer 2

R  = $12800(1 + r) ^{n}$

  Since r is half yearly.
 so we have to take the interest at half yearly basis.  r is interest per 6 months.  in 18 months, we have half years.  So interest is 3 times. 
 so  n = 3

R = 12800 + 2017.60 = Rs  14817.60

So 14817.60 = 12800  (1+r)³           

  so (1+r)³ =  14817.60 / 12800  
 
So 1 + r = 1.05 

 =>  r = 0.05 

=>  r = 5 %

Rate for 6 months is 5% so per annum = 2 x 5 = 10 %