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Question 1045551: 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 13% per year or in a certificate of deposit (CD) paying 3% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the amount invested in b rated bonds.
let y = the amount invested in certificates of deposit.
x + y = 50000
this means that the total investment must be equal to 50,000 dollars.
.13x + .03y = 6000
this means that the total interest must be equal to 6,000 dollars.
these are 2 equations that need to be solved simultaneously.
i will solve by elimination.
start with:
x + y = 50000 (first equation)
.13x + .03y = 6000 (second eauation)
multiply both sides of the first equation by 13 and multiply both sides of the second equation by 100 to get:
13x + 13y = 650000
13x + 3y = 600000
subtract the second equation from the first to get 10y = 50000.
divide both sides of that equation by 10 to get y = 5000
since x + y = 50000, then x must be equal to 45000.
your solution should be that 45000 must be invested at 13% and 5000 must be invested at 3%.
.13 * 45000 + .03 * 5000 = 6000.
the solution looks good.
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