A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per ye

A retired couple has $160,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. How much should they invest in each to realize exactly $15,600 per year?

SOLUTION

To solve this problem we take a given amount  to be invested in AA bonds as x  with interest of 11% (0.11) thus the one left (160000-x) was invested in safe certificate of deposit yielding with interest of 6%(0.06) to get a total interest of 15600.

Therefore 0.11x + (160000-x) 0.06 = 15600

0.11x + 9600 -0.06x = 15600 collect like terms together,

0.11x - 0.06x = 15600-9600

0.05x = 6000

0.05x/0.05= 6000/0.05, x=120000

And 160000-x = 160000-120000 = 40000 thus the amount to be invested in safe certificate of deposit yielding is 40000 and amount to be invested in AA bonds is 120000 to realize exactly $15,600 per year.