investing and interest

Question

Besty,a recent retiree, requires $5,000 year in extra income. She has $70,000 to invest and in B-rated bonds paying 15% a year or in a certificate deposit (CD) paying 7% a year. how much should be invested in each to realize exactly $5000 in interest per year?

Answer 1

Let x = the amount to invest in B-rated bonds

And let y = the amount to invest in the CD

 

Since the total being invested is 70000, that gives us a simple equation:

 

x + y = 70000

 

Now, how much will be earned from the B-rated bonds?  Since the interest is 15% and the amount invested is x, the interest will be 15% of x, or 0.15 x.

 

Similarly, the amount of interest from the CD will be .07 y

 

We want the total interest to be 5000, so that gives us another equation:

 

0.15 x + .07 y = 5000

 

Solve these two equations.  The easiest way is this case is with substitution.

 

From the first equation, you can figure out that y = 70000 - x

 

So substitute that into the second equation:

0.15 x + .07 y = 5000

0.15 x + .07 (70000 - x) = 5000

0.15 x + 4900 - .07 x = 5000

 

0.08 x + 4900 = 5000

0.08 x = 100

x = 1250

 

Since y = 70000 - x, that means that y = 68750

 

So 1250 should be invested in B-rated bonds, and 68750 in the CD.