Question

30. কোনাে টাকার জটিল সুদে প্রথম বছরে 650 টাকা এবং দ্বিতীয় বছরে 676 টাকা হলে,
আসল কত?​

Answer 1

Given :- A sum of money invested at compound interest amount to rupees 650 at the end of 1st year and rupees 676 and the end of second year the sum of the money is ?

Solution :-

Let the sum is Rs.P and rate is R% per annum .

so,

→ Amount after 1 year = P[1 + (R/100)] = Rs.650 ---- Eqn.(1)

and,

→ Amount after 2 years = P[1 + (R/100)]² = Rs.676 ----- Eqn.(2)

putting value of Eqn.(1) in Eqn.(2) ,

→ 650[1 + (R/100)] = 676

→ [1 + (R/100)] = 676/650

putting this value in Eqn.(1),

→ P * (676/650) = 650

→ 676P = 650 * 650

→ P = (650 * 650)/676

→ P = Rs.625 (Ans.)

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Answer 2

Given :  Amount at compound interest become 650 after 1 year and 676 after 2 years

To Find :  Initial Amount

Solution:

Initial Amount = P

Rate of interest = R

Amount after 1 year = P ( 1 + R/100)  = 650  Eq1

Amount after 2 year  = P ( 1 + R/100)² = 676   Eq2

Squaring Eq1 both sides

=> P² ( 1 + R/100)²  = (650)²

=> P * P ( 1 + R/100)² = (650)²

Substituting  P ( 1 + R/100)² = 675 from Eq2

P * 675  = (650)²

=> P = (650)² / 676

=> P = ( 25 * 26)² / 26²

=> P = 25²

=> P = 625

Initial Amount = 625

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