Question

Maria has recently retired and requested an extra ​$444.00 per year in income. She has $ 5400 to invest in an​ A-rated bond that pays 10 % per annum or a​ B-rated bond paying 6 % per annum. How much should be placed in each investment in order for Maria to achieve her​ goal?

Answer 1

$2400 in A rated bond and $3000 in B rated bond.

Explanation:

We have been given that Maria has recently retired and requested an extra ​$444.00 per year in income.

We can represent this information in an equation as:

`A+B=5400...(1)`

She has $5400 to invest in an​ A-rated bond that pays 10% per annum or a​ B-rated bond paying 6% per annum.

`0.10A+0.06B=444...(2)`

From equation (1), we will get:

`A=5400-B`

Substitute this value in equation (2):

`0.10(5400-B)+0.06B=444`

`540-0.10B+0.06B=444`

`540-0.04B=444`

`540-540-0.04B=444-540`

`-0.04B=-96`

`(-0.04B)/(-0.04)=(-96)/(-0.04)`

`A=2400`

Therefore, Maria should invest $2400 in A-rated bond.

Substitute
`A=2400` in equation (1):

`2400+B=5400`

`2400-2400+B=5400-2400`

`B=3,000`

Therefore, Maria should invest $3000 in B-rated bond.