suppose you invest a certain amount of money n an account that pays 11% interest annually, and 4000 more than that in an account that pays 12% annually, How much money do you have in each account id the total interest for a year is 940
let the amount invested at 11% be x
so .11x + .12(x+4000) = 940
.11x + .12x + 480 = 940
.23x = 460
x = 2000
So originally you had
$2000 in the 11% account and
$6000 in the 12% account
at the end you had 2220 and 6720 respectively
check: 2220+6720-8000 = 940
Let's assume the amount of money invested in the account that pays 11% interest annually is x.
According to the information given, the amount of money invested in the account that pays 12% interest annually is x + 4000.
We can calculate the interest earned in each account using the formula:
Interest = Principal * Rate
For the account that pays 11% interest:
Interest_11% = x * 11/100
For the account that pays 12% interest:
Interest_12% = (x + 4000) * 12/100
The total interest earned for a year is given as $940. So, we can write the equation:
Interest_11% + Interest_12% = 940
Substituting the expressions for interest from above, we get:
(x * 11/100) + ((x + 4000) * 12/100) = 940
Now, let's solve this equation to find the value of x.
To solve this problem, we can break it down into two equations. Let's assume the amount of money invested in the account that pays 11% interest is x, and the amount invested in the account that pays 12% interest is (x + 4000).
To calculate the interest earned in each account, we'll use the formula:
Interest = Principal * Rate
For the account that pays 11% interest, the interest earned would be:
0.11x
For the account that pays 12% interest, the interest earned would be:
0.12(x + 4000)
Now, according to the given information, the total interest earned is 940. So, we can set up the equation:
0.11x + 0.12(x + 4000) = 940
Let's solve this equation step by step:
1. Distribute the 0.12 to the terms inside the parentheses:
0.11x + 0.12x + 480 = 940
2. Combine the like terms:
0.23x + 480 = 940
3. Subtract 480 from both sides of the equation:
0.23x = 460
4. Divide both sides of the equation by 0.23:
x = 2000
We have found the amount invested in the account that pays 11% interest is $2000.
Now, we can find the amount invested in the account that pays 12% interest:
(x + 4000) = (2000 + 4000) = $6000
So, the amount of money in each account is $2000 in the 11% interest account and $6000 in the 12% interest account.