Results 1 to 2 of 2

Math Help - investor

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    106

    investor

    An investor has $10000 to invest in 3 types of bonds: short-term, intermediate-term and long-bond term. Short term bonds pay 4% annually, intermediate term bonds pay 6%, and long terms bonds pay 8%. The investor wishes to have a total annual return of $6700 on her investment, with equal amounts invested in intermediate and long term bonds. How much should she invest in each type?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,240
    Thanks
    1795
    Quote Originally Posted by aeroflix View Post
    An investor has $10000 to invest in 3 types of bonds: short-term, intermediate-term and long-bond term. Short term bonds pay 4% annually, intermediate term bonds pay 6%, and long terms bonds pay 8%. The investor wishes to have a total annual return of $6700 on her investment, with equal amounts invested in intermediate and long term bonds. How much should she invest in each type?
    Start by naming your variables: Let x bet the amount of money invested in short term bonds, y the amount of money invested in intermediate term bonds, z the amount of money invested in long term bonds.

    "An investor has $10000 to invest":
    x+ y+ z= 10000.

    "The investor wishes to h ave a total annual return on her investment."
    The return on any one amount is the amount invested times the percentage return: .04x, .06y, and .08z for each so the total is .04x+ .06y+ .08z=6700.

    "with equal amounts invested in intermediate and long term bonds": y= z.

    You have three equations in the three unknowns x, y, z:
    x+ y+ z= 10000
    .04x+ .06y+ .08z= 6700
    y= z.

    Since y= z, you can replace z by y in the first two equations:
    x+ y+ y= x+ 2y= 10000
    .04x+ .06y+ .08y= .04x+ .14y= 6700

    From x+ 2y= 10000, you can get x= 10000- 2y and replace that in the last equation:
    .04(10000- 2y)+ .14y= 6700.

    Solve that equation for y and then work back to find x and z.

    Don't forget to write your final answer as a complete sentence. You can't just say x= ..., y=..., z= ... because whoever gave you this problem doesn't know what "x", "y", and "z" mean.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum