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

Answer:

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

Step-by-step 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):

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

$540-0.10B+0.06B=444$

$540-0.04B=444$

$540-540-0.04B=444-540$

$-0.04B=-96$

$\frac{-0.04B}{-0.04}=\frac{-96}{-0.04}$

$A=2400$

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.