Phyllis invested 57000 dollars,

Question

Phyllis invested 57000 dollars, a portion earning a simple interest rate of 5 percent per year and the rest earning a rate of 7 percent per year. After one year the total interest earned on these investments was 3290 dollars. How much money did she invest at each rate?

At rate 5 percent :
At rate 7 percent :

Answer 1

Treena,

For this problem, we need to use the basic interest formula, I=Prt (Interest equals principal multiplied by rate multiplied by time). We are told that the investment is for 1 year (t) and that the interest is $3,290 (I). The concern is that there are two rates and we do not know how much of our principal is applied to each rate. We must set our variables:

For our first rate of 5%, we will use a variable of x for our principal

For our second rate of 7%, our variable becomes 57,000-x (since the two variables must add to 57,000)

 

Now we can create our equation. We must note each investment separately in the equation;

         I=Prt+Prt

         3,290=x(.05)1 + (57,000-x).07(1)

         3,290=.05x+3,990-.07x

         3,290=3,990-.02x

         -700=-.02x

         35,000=x Remember that x is the investment at 5%.

So now we can solve for our second investment;

         7% Investment: 57,000-x

                                 57,000-35000=22,000