Set up and solve an inequality to answer this question

Question

Melissa is planning to invest a total of $17,000 in two accounts. If she invests $10,000 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 $1900 in yearly simple interest?

Answer 1

For simple interest I = prt

Interest = principle*rate*time

 

An investment of 10,000 at 12% yields

I = 10,000(.12)(1) = $1,200 interest

 

We need the other $7,000 to yield at least $700

in order for the annual interest to be at least $1900

 

The inequality for the interest to be at least $700 will be

 

prt ≥ 700

 

7000(r)(1) ≥ 700

7000r ≥ 700

r ≥ 700/7000

r  ≥ .1

 

The interest rate must be a minimum of 10% on the 2nd investment

Answer 2

Melissa,

The interest payout for simple interest is found by the equation: I = Prt

I - interest

P - principle

r - rate

t - time

 

The 12% on 10k is: I = 10000(.12)1 = $1200.00

 

1900 - 1200 = 700 to be earned by the other investment.

17000 - 10000 = 7000 for the second investment.

 

700 = 7000r(1)

.10 = r

 

The second investment must earn 10%