Solve the problem

Question

A 84,000 trust is to be invested in bond paying 8%, CDs passing 7% and mortgages paying 9%. The soon is the bond and CD investment must equal the mortgage investment. To earn an $7010 annual income from the investments, how much should the bank invest in bonds?

Answer 1

 

We can get three equations from the word problem:

First, we know that the three amounts in the three investments add up to a total of 84000.

1) B + C + M = 84000

 

Second, we know that the sum of the two investments in bonds and CDs is equal to the investment in the mortgages.

2) B + C = M

B + C - M = 0

 

Third, we know that the amount of the investments, at given percentages, returns 7010.

3) .08B + .07C + .09M = 7010

 

 

Now we just have to combine the three formulas to solve for the variables.

 

4) Start by subtracting formula 2 from formula 1.

 

B + C + M = 84000

-B - C + M = 0

2M = 84000

M = 42000

 

5) Next, multiply formula 2 by -.07 and subtract it from formula 3.

.08B + .07C + .09M = 7010

.07B -.07C +.07M = 0

.15B + .16M = 7010

 

Now substitute the value for M in formula 4 into formula 5 and we can solve for another variable.

 

.15B + .16(42000) = 7010

.15B + 6720 = 7010

.15B = 290

B = 1933.33

 

Finally, insert the two variables we have into formula 1 to get the third variable.

C = 40066.67

 

 

Hope this helps, Joshua!  If you'd like online tutoring in Algebra, let me know.