# A certain amount of money was put in the bank. A year later, 0.25 of the initial amount was withdrawn from the account

**A certain amount of money was put in the bank. A year later, 0.25 of the initial amount was withdrawn from the account, and a year later, the deposit amounted to 0.935 of the original amount. Find bank interest.**

Let S be the amount of money deposited in the bank.

р% – interest that the bank calculates per year.

Account status after a year:

S + S * p / 100;

Account balance after withdrawing 25% of the original amount:

S + S p / 100 – S 25/100 = 0.75 S + S p / 100;

Account status after two years:

(0.75 S + S p / 100) + (0.75 S + S p / 100) p / 100 = 0.935S.

Reduce the expression by S and multiply by 10000.

7500 + 100p + 75p + p ^ 2 = 9350;

7500 + 175 p + p ^ 2 – 9350 = 0;

p ^ 2 + 175 p – 1850 = 0;

find the roots by Vieta’s theorem.

p1 p2 = -1850;

p1 + p2 = -175;

p1 = -185 – does not meet the conditions of the problem.

p2 = 10.

Answer: The bank interest is 10.