How to Solve "Interest" Problems

Problem:
Mr. McGregor invested $10,000.  Part of it he put in the bank at 5% interest.  The remainder he put in bonds which paid a 9% yearly return.  How much did he invest in each if his yearly income from the two investments was $660?

Steps:

1. Model the problem
   
   Let               x = amount invested at 5% worth .05(x) dollars
          10,000 - x = amount invested at 9% worth .09(x) (10,000 - x) dollars
     

2. Write the equation for the problem using the information contained in Step 1 and in the problem.
   
   .05(x) + .09 (10,000 - x) = 660
     

3. Solve the equation contained in Step 2.
   

   .05(x) + .09(10,000 - x)	= 660
   .05x + 900 - .09x	= 660
   -.04x + 900	= 660
   +.04x - 660	-660 + .04x
   240	= .04x
   240	= .04x
   .04	.04
   6000	= x
   x	= 6000
   10,000 - x	= 4000

    

4. Be sure that the solution you obtained, answers the question given in the problem.

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