Question 1137202: Betsy, a recent retiree, requires $6,000 per year in extra income. She has $60,000 to invest and can invest in B-rated bonds paying
13% per year or in a certificate of deposit (CD) paying
5% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) Algebraically....
x amount at 13% and the rest of the $60,000 at 5%; the total interest is the sum of the amounts of interest from each investment:
Basic algebra; complicated a bit by the decimals; I leave it to you to find the solution by that method.
(2) A much easier and faster way to solve "mixture" problems like this....
(a) The $6000 interest she wants is 10% of the $60,000.
(b) 10% is 5/8 of the way from the lower percentage of 5% to the higher percentage of 13%. (13-5 = 8; 10-5 = 5; so 10% is 5/8 of the way from 5% to 13%).
(c) That means 5/8 of the money needs to be invested at the higher rate.
ANSWER: 5/8 of $60,000 = $37,500 at 13%; the rest, $22,500, at 5%.
CHECK:
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