maria has recently retired and requires an extra $7200 per year income. she has $120000 to invest in an Aaa-rated bond that pays 5% per annum or a B-rated bond paying 10% per annum. how much should be placed in each investment in order for Maria to achieve her goal?
To determine how much should be placed in each investment, we need to set up an equation.
Let's assume Maria places x dollars in the Aaa-rated bond earning 5% per annum. Since she has $120,000 in total, the amount invested in the B-rated bond earning 10% per annum will be (120,000 - x).
Now, let's calculate the income Maria will receive from each investment.
For the Aaa-rated bond, the annual income can be calculated as 5% of the amount invested:
Annual income from Aaa-rated bond = (5/100) * x
For the B-rated bond, the annual income can be calculated as 10% of the amount invested:
Annual income from B-rated bond = (10/100) * (120,000 - x)
Maria wants her total annual income to be $7,200. Therefore, we can set up the following equation:
(5/100) * x + (10/100) * (120,000 - x) = 7,200
Now, let's solve this equation to find the values of x and (120,000 - x).
(5/100) * x + (10/100) * (120,000 - x) = 7,200
Simplifying the equation:
0.05x + 0.1 * (120,000 - x) = 7,200
0.05x + 12,000 - 0.1x = 7,200
0.05x - 0.1x = 7,200 - 12,000
-0.05x = -4,800
Dividing both sides by -0.05:
x = 4,800 / 0.05
x = 96,000
Therefore, Maria should place $96,000 in the Aaa-rated bond and $24,000 (120,000 - 96,000) in the B-rated bond in order to achieve her goal of receiving an extra $7,200 per year income.