Question

The difference between the compound interest and simple interest on a certain sum of money at 15% per annum for 3 years is rupees to 283.50 .Find the sum.

Answer 1

Answer:

Step-by-step explanation:

Hey there this is the answer....

Answer 2

Answer:

The sum of the money = 4000 Rs.

Given data:

Difference between the compound interest and simple interest of the sum of money  = 283.50 Rs

rate of interest on both compound and simple interst = 15%

Given time period for both compound and simple interest = 3 year  

Here we need to find the sum of the money

Step-by-step explanation:    

Let x be the sum of the money        

Compound interest on sum of the money  

here  P = x,  r = 15%  and t = 3 years  

compound interest  = $p(1+\frac{r}{100} )^{t} - p$  

                                 = $x(1+\frac{15}{100} )^{3} - x$  

                                 = $x(\frac{115}{100} )^{3} - x$    

                                 = $x( 1.15 )^{3} - x$    

                                 = $1.520875x - x$  

                                 =  0.520875x

simple interest on the sum of the money    

here P = x, R = 15%  and  T = 3 years  

simple interest   = $\frac{PTR}{100 }$  = $\frac{x(15)(3)}{100}$  = $\frac{x(3)(3)}{20}$  = $\frac{9x }{20}$  = 0.45x    

⇒ difference between compound interest and simple interest = 283.50    

                   0.520875x - 0.45x  = 283.50    

                                 0.070875x = 283.50

                                                  x = 4000