Question

The difference between simple and compound interest compound compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1 the sum in rupees is

Answer 1

Answer: 625 Rs.

Step-by-step explanation:

For difference between C.I and S.I for 2 years the following formula apply.

Difference = P[R/100]²  , where P = sum , R = rate %

1 = P[4/100]²

1 * 100 *100/ 4*4 = P

25*25 = P

P = 625 Rs.

ALTERNATE:

The difference for 2 years is always the 'interest earned on 1st years simple interest'

So, 4% of simple interest = 1

4/100 * simple interest = 1

simple interest = 25

Now, 4% of sum = 25

4/100 * sum = 25

sum = 100*25/4 = 625

CONCEPT:

S.I for 2 years = S.I + S.I    [interest for each year is same]

C.I for 2 years = S.I + S.I +R*S.I/100  [every year we receive the simple interest and the subsequent interest of previous years simple interest]

Answer 2

Answer:

₹625

Step-by-step explanation:

Let us take the  principal to be = P

P(1+4/100)^2 = P(104/100)^2 = P(52/50)^2

Total amount after two years with S.I =

P+Px2 x 4/100 = P(1+8/100) - P(54/50)

Given that the difference is ₹1

P(52/50)^2 - P(54/50)^2 = 1

P/50(52 x 52/50 - 54) = 1

P/50 ( 52 x 52 -54 x 50/50) = 1

P(2704 - 2700) = 2500

4P = 2500 = P=2500/4 = ₹625