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Question

John invested a total of $5000, part at 3% simple interest and part at 4% simple interest. At the end of 1 year, the investments had earned $176 interest. How much was invested at each rate?

Answer 1

For simple interest:

 

Interest = Principle*Rate*Time

 

Let x be the amount of the principle that John invests at 3% (0.03).  The interest he earns at 3% is:

 

Interest at 3% = x*(0.03)*(1 year) = (0.03)x

 

Since his total investment is $5000, the amount John invests at 4% (0.04) is $5000-x.  The interest at 4% is:

 

Interest at 4% = ($5000-x)*(0.04)*(1 year) = $200 - (0.4)x

 

The total interest earned is:

 

Total Interest = Interest at 3% + Interest at 4%

$176 = (0.03)x + $200 - (0.04)x

-$24 = -(0.01)x

$2400 = x

 

John invests $2400 at 3% and $5000 - $2400 = $2600 at 4%.