Help please

Question

A retired couple has $180,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 7%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $17,400 per year?

Answer 1

We will say x is how much they will place into Cert. of Dep. and therefore (180,000 - x) is what they will place into AA bonds.

 

Since the Cert of Dep yields 7% then they earn 0.07 times x.

 

Since the AA bonds yield 11%, then they earn 0.11 times (180,000 - x).

 

Since their goal is 17,400, then we can make an equation

 

0.07x + 0.11(180,000 - x) = 17,400.

 

Distribute and we get : 0.07x + 19800 - 0.11x = 17,400

 

Simplfiy and we get 19,800 -0.04x = 17,400

 

add the 0.04x to the right and subtract 17,400 to the left and we get

 

2400 = 0.04x

 

Divide by 0.04 and x = 60,000. 

 

Therefore $60, 000 will be invested in the Cert of Dep.

and 180,000 - 60,000 = $120,000 will be invested in the AA bonds.