Question

Find the sum invested at 10%C.I compounded annually on which the interest for the third year exceeds the interest of the first year by₹256

Answer 1

Answer:

Let intial amount is P

Given,

rate of interest , r = 10%

C.I for the 3rd year = 256 + C.I for the 1st year

Now, C.I for the 3rd years = amount after 3 years - amount after 2 years

= P(1 + r/100)³ - P(1 + r/100)²

= P(1 + 10/100)³ - P(1 + 10/100)²

= P(11/10)³ - P(11/10)²

= P(1331/1000 - 121/100)

= 121P/1000

And C.I for 1st year = S.I of 1st year = P × r × 1/100

= P × 10/100 = P/10

Now, 121P/1000 = 256 + P/10

⇒ 121P/1000 - P/10 = 256

⇒(121 - 100)P/1000 = 256

⇒ 21P = 256 × 1000

⇒ P = 12190.4762

Hence initial amount = 12190.4762 Rs