SOLUTION: Cara wants to invest $16,000 in certificates of deposit (CDs). For tax purposes, she wants her total interest per year to be $900. She wants to put $1000 more in a 2-year CD than i

Algebra ->  Finance -> SOLUTION: Cara wants to invest $16,000 in certificates of deposit (CDs). For tax purposes, she wants her total interest per year to be $900. She wants to put $1000 more in a 2-year CD than i      Log On


   

Question 1188040: Cara wants to invest $16,000 in certificates of deposit (CDs). For tax purposes, she wants her total interest per year to be $900. She wants to put $1000 more in a 2-year CD than in a 1-year CD and invest the rest in a 3-year CD. How much money should she invest in each type of CD?
_________________________________________
| Number of Years: 1 | 2 | 3 |
| ________________________|______|______|
| Rate of Interest: 3.0% | 5.0% | 6.0% |
|_________________________|______|______|
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

x         = invested at 3%;

(x+1000)  = invested at 5%;

the rest,  (16000-x-(x+1000)) = 15000-2x invested at 6%.


The total 1-year interest 


    0.03x + 0.05(x+1000) + 0.06(15000-2x) = 900.


Simplify and find x


    0.03x + 0.05x + 50 + 900 - 0.12x = 900


    0.03x + 0.05x - 0.12x = 900 - 50 - 900


           -0.04x         = -50


              x           = %28-50%29%2F%28-0.04%29 = 1250  dollars.


ANSWER.  $1250 invested  at 3%;  $2250 invested at 5%;  and the rest, 16000-1250-2250 = 12500 invested at 6%.


CHECK.  0.03*1250 + 0.05*2250 + 0.06*12500 = 900 dollars, the total annual interest.  ! Precisely correct !

Solved.