Daniel deposit a certain sum of money in a bank.if the simple interest rate of the bank decreases from 15/4% and 7/2% per annum, Daniel interest will increase by $50 in a year . Find the sum of money he deposits
Let the sum of money that Daniel deposits be x.
According to the problem, the increase in interest when the rate decreases from 15/4% to 7/2% is $50.
So, the interest at 15/4% per annum is [(15/4)/100]*x = 15x/400
And the interest at 7/2% per annum is [(7/2)/100]*x = 7x/200
Given that the increase in interest is $50 in a year, we can form the equation:
(7x/200) - (15x/400) = 50
Now, let's solve this equation.
Multiply both sides of the equation by 400 to get rid of the denominators:
2*(7x) - (15x) = 200 * 50
14x - 15x = 10000
-x = 10000
Divide both sides by -1:
x = -10000
Since the amount of money deposited cannot be negative, the value of x can be disregarded.
Therefore, there is no valid solution to this problem.
Let's assume the initial deposit amount as 'x' dollars.
At a simple interest rate of 15/4% per annum, the interest earned would be (15/4)x/100 dollars.
At a simple interest rate of 7/2% per annum, the interest earned would be (7/2)x/100 dollars.
According to the problem, the difference between these two interests in a year is $50.
(15/4)x/100 - (7/2)x/100 = $50
Multiplying the whole equation by 100 to eliminate the denominators:
(15/4)x - (7/2)x = 50 * 100
(15/4 - 7/2)x = 5000
(30/8 - 28/8)x = 5000
(2/8)x = 5000
(1/4)x = 5000
x = 5000 * 4
x = 20000
Therefore, Daniel deposits $20,000 in the bank.