Question

A retired woman has 70,000toinvestbutneedstomake

9,000 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 $9,000 annual return.

Answer 1

• $51,250 at 15%
• $18,750 at 7%

Explanation:

The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.

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setup

Let x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...

0.15x +0.07(70000-x) = 9000

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solution

Simplifying the equation gives a 2-step linear equation.

0.08x +4900 = 9000 . . . . simplified

0.08x = 4100 . . . . . . . . . . subtract 4900

x = 51,250 . . . . . . . . . . . .divide by 0.08

70000 -x = 18,750

The woman should invest $51,250 at 15% and $18,750 at 7%.