Question 1207734: Betsy, a recent retiree,requires $6000 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 $6000 in interest per year?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The solution in the link provided by the other tutor shows the standard method for solving a problem like this.
If a formal algebraic solution is not required, here is a solution that uses a method that can be used to solve ANY 2-part "mixture" problem like this.
(1) Betsy wants a $6000 return on her investment of $50,000. Do some mental arithmetic to see that the required interest rate is 12%.
(2) Compare the three interest rates 7%, 12%, and 15% (on a number line, if it helps) and observe/calculate that 12% is 5/8 of the way from 7% to 15%.
(3) That means 5/8 of the $50,000 must be invested at the higher rate.
5/8 of $50,000 = 5 * $6250 = $31,250
ANSWER: $31,250 at 15%, the other $18,750 at 7%.
CHECK: .15($31250)+.07($18750)=$4687.50+$1312.50=$6000
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