SOLUTION: Using simple interest, a foundation invests ​$65,000: a part at 7​%, twice that amount at 4​%, and the rest at 5.5​%. What is the most that the foundation can invest at 4β€

Algebra ->  Finance -> SOLUTION: Using simple interest, a foundation invests ​$65,000: a part at 7​%, twice that amount at 4​%, and the rest at 5.5​%. What is the most that the foundation can invest at 4†     Log On


   

Question 1146612: Using simple interest, a foundation invests ​$65,000: a part at 7​%, twice that amount at 4​%, and the rest at 5.5​%. What is the most that the foundation can invest at 4​% and be guaranteed ​$3500 in interest per​ year?
The foundation can invest at most ​____ at 4​%.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
7% interest account:
Principal = p/2
Rate = 0.07
Interest = 0.07p/2 = 0.035p

4% interest account:
Principal = p
Rate = 0.04
Interest = 0.04p

5.5% interest account:
Principal = 65000 - p/2 - p
Rate = 0.055
Interest = 0.055(65000 - p/2 - p) = 3575 - 0.0275p - 0.055p = 3575 - 0.0825p

0.035p + 0.04p + (3575 - 0.0825p) >= 3500

-0.0075p + 3575 >= 3500

-0.0075p >= -75

p <= 10000

4% interest:
Principal = p <= 10000

The most you can invest in the 4% interest account is $10,000.