Lesson Typical investment problems

Typical investment problems

Problem 1

Let x = amount invested at 9%, in dollars.

Then the amount at 6% is the rest (10000-x) dollars.



The interest from the 9% amount is 0.09*x  dollars.

The interest from the 6%   amount is 0.06*(10000-x)   dollars.



Your equation is


    interest + interest      = total interest,   or


    0.09*x  + 0.06*(10000-x) = 810   dollars.


From the equation, express x and calculate the answer


    x =  = 7000.


Answer.  The amount at 9% is $7000;  the rest  $10000-$7000 = $3000 is the amount at 6%.


Check.   0.06*3000 + 0.09*7000 = 810 dollars.   ! Correct !

Problem 2

Let x be the amount invested at 8%, in dollars.

Then the amount invested at 6% is (22500-x) dollars.


The annual interest produced by the 8% account is 0.08x  dollars.

The annual interest produced by the 6% account is 0.06*(22500-x)  dollars.

The total annual interest is the sum  0.08x + 0.06*(22500-x)  dollars.


Write an equation for the total annual interest

    0.08x + 0.06*(22500-x) = 1420  dollars.


Simplify this equation and find x

    0.08x + 0.06*22500 - 0.06x = 1420

    0.08x - 0.06x = 1420 - 0.06*22500

         0.02x    =      70

             x    =      70/0.02  

             x    =      3500.


ANSWER.  $3500 was invested at 8% and the rest  22500-3500 = 19000 dollars was invested at 6%.


CHECK.   0.08*3500 + 0.06*19000 = 1420  dollars,  total annual interest.   ! correct !