Help. Inequality word problem.

[cmorton557]

Christine is planning to invest a total of \$21,000 in two accounts. If she invests \$13,000 in a CD paying 12% annual simple interest, at what rate does the remainder of her money need to be invested so that the two investments together yield at least \$2520 in yearly simple interest? (Set up and solve an inequality to answer this question).

[HallsofIvy]

If she invests 13000 in a CD paying 12% then it returns (0.12)(13000)= 1560 annually. If she invests the remaining 8000 at rate r then that returns r(8000). That total will be 1560+ 8000r which you want to be 2520 or more. That is, you want to solve the inequality $8000r+ 1560\ge 2520$.

[mycalsuite]

The simple interest formula I=P×r×t is applied in this issue.

I stands for interest earned.

P is the principal (amount invested).

r = interest rate per year

Time in years is represented by t.

Since both investments have a one-year duration, t = 1.
Since the total interest must be at least (≥) $2520, we next create an inequality.

We determine the lowest rate r that meets the requirement by adding the interest from both accounts.
The outcome demonstrates that, in theory, both investments must generate an overall average rate of 12%, meaning that the second investment must likewise be at least 12%.