A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $6,000 annual return

Question

A retired woman has $50,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%.

Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $6,000 annual return

Hero · Answer

Let x represent the amount of money in one bond
and y represent the amount of money in the certificate of deposit

Then we can set up the following system:
              x + y = 50000
0.15x + 0.07y = 6000

After some manipulation we have:
15x + 7y = 600000
  7x + 7y = 350000

After subtraction we have:
8x = 250000

Solving for x and y yields:
x = 31250
y = 18750

So $31,250 should be invested in the bond and $18,750 should be invested in the certificate of deposit.

Let's check this:
              31250 + 18750 = 50000
.15(31250) + .07(18750) = 6000
        4687.50 + 1312.50 = 6000

Hero · Answer

@psirockin2 do the amounts you come up with sum to $50,000