Solve the problem. Helen Weller invested $15,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the total interest is equal to the interest on the two investments at the rate of 13%?
$5500.
Set up the equations like this
(11,000*.12)+(x*.15)=(11,000+x).13
1320+ .15x=1430+ .13x
.02x=110
x= 5500
by Ali :)
To solve this problem, we need to find the additional amount of money that needs to be invested in the second account.
Let's break down the information given:
1. Helen invested $15,000 in an account that pays 12% simple interest. This means that the interest earned on this investment can be calculated as 12% of $15,000.
2. We need to find the additional amount that needs to be invested in the second account, which pays 15% simple interest.
3. The total interest earned from both investments should be equal to the interest earned on the two investments at the rate of 13%.
Now, let's calculate the interest earned from the first investment:
Interest from the first investment = 12% of $15,000
= (12/100) * $15,000
= $1,800
Next, let's assume the additional amount to be invested in the second account is 'X'. We can express this as:
Interest from the second investment = 15% of X
= (15/100) * X
Now, we know that the total interest should be equal to the interest earned on the two investments at the rate of 13%. Therefore, we can set up the equation:
$1,800 + (15/100) * X = 13% of ($15,000 + X)
To solve this equation for X, we can follow these steps:
1. Convert 13% into its decimal form: 13/100 = 0.13
2. Distribute 0.13 to ($15,000 + X): 0.13 * ($15,000 + X) = 0.13 * $15,000 + 0.13 * X
3. Simplify the equation:
$1,800 + (15/100) * X = 0.13 * $15,000 + 0.13 * X
4. Group like terms:
(15/100) * X - 0.13 * X = 0.13 * $15,000 - $1,800
5. Combine the terms:
(15/100 - 0.13) * X = $1,950
6. Simplify the equation:
(0.02) * X = $1,950
7. Divide both sides of the equation by 0.02:
X = $1,950 / 0.02
Now, using a calculator, we can find the value of X:
X = $97,500
Therefore, an additional $97,500 must be invested in the account that pays 15% simple interest so that the total interest is equal to the interest on the two investments at the rate of 13%.