Question

At what rate percent the difference of compound interest and simple interest on a certain sum of Rs. 40,000 in 3 years is Rs. 305?​

Answer 1

Step-by-step explanation:

Let the sum be Rs.100

Computation of compound interest:

Prinicpal =Rs.100

R=10% per annum and n=2 years.

Amount=Rs.⎣⎢⎡100×(1+10010)2⎦⎥⎤

                =Rs.⎣⎢⎡100×(211)2⎦⎥⎤=Rs.121

Computation of simple interest:

Prinicpal =Rs.100

R=10% and Time =2 years.

∴S.I.=Rs.(100100×10×2)=Rs.20

Thus, difference in C.I. and S.I.=Rs.(21−20)=Re.1

Now, if difference between C.I and S.I. is Re.1,    Then Sum =Rs.100

If difference between C.I. and S.I. is Rs.500,    Then Sum =Rs.(100×500)=Rs.50000

Answer 2

A = p(1+r)³ = p(1+r³+3r²+3r)

CI = A -P

As = p(1+3r)

SI = As - P

CI - SI = A - As

=p((1+r)³-1-3r)

= p(r³+3r²)

305 = 40000(r³+3r²)

76.25×10^(-4) =r³+3r²

r³ is negligent

7625×10^(-6) =3r²

r = 0.05

r= 0.05×100 =5%