Question

The difference between compound interest and simple interest on a certain sum of money at 10% per annum for 2 years is rs.40/-. the sum is

Answer 1

Simple Interest = PRT / 100

Let Principal be P

So,

SI = (P x 10 x 2) /100

SI = P/5

Compound Interest = P [( 1 + r/100 )^t  - 1 ]

CI = P [ (1 + 10/100)^2 - 1 ]

CI = P [ ( 1.1 ) ^2 -1 ]

CI = P ( 1.21 - 1)

CI = 0.21 P

We are given, CI - SI = 40

So,

0.21 P - P/5 = 40

1.05 P - P = 200

0.05 P = 200

P = 200/0.05

Principal or Sum = 4000

Answer 2

Hello Dear.

Here is the answer---


Let the Sum of Money be Rs. P.

Given ⇒
Rate of Interest(R%) = 10%
Time(T) = 2 years.

Now,
∵ Simple Interest (S.I.) = (P × R × T)/100
 = (P × 10 × 2)/100
 = P/5

Now, Compound Interest = A -  P.
 = P(1 + r%/100)ⁿ - P
= P(1 + 10/100)² - P
= P(11/10)² - P
= P(121/100 - 1)
= P(21/100)
= 21P/100


According to the Question,

   C.I. - S.I. = 40
⇒ 21P/100 - P/5 = 40
⇒ 21P - 20P = 40 × 100
⇒ P = 4000
⇒ P = Rs. 4000 


∴ Sum of the Principal(P) is Rs. 4000.


Hope it helps.