betsy, a recent retiree requires $6,000 per year in extra income. she has $50,000 to invest and can invest in b rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. how much money should be invested in each to realize exactly $6,000 in interest per year? [please explain and show steps so i can study it ^_^]

Question

betsy, a recent retiree requires $6,000 per year in extra income. she has $50,000 to invest and can invest in b rated bonds paying 15% per year or in a certificate of deposit (CD)  paying 7% per year. how much money should be invested in each to realize exactly $6,000 in interest per year? [please explain and show steps so i can study it ^_^]

lyrae · Answer

You have to make a system of equations:
Lets assume x is the amount invested in bonds and y the amount invested in CD.
We know that we cannot invest more money than we have so: 
50000 = x + y
we also know how much the return should be:
6000 = 1.15x + 1.07y

Now all you have to do is slove this system of equations:
50000 = x + y
6000 = 1.15x + 1.07y
and you'll have your answer.