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Question 1206271: 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 17% 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?
Found 3 solutions by Theo, greenestamps, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! she needs 6000 per year.
she has:
50,000 total to invest.
b-rated bonds pay 17% per year
certificates of deposit pay 7% per year.
let x = value in b-rated bonds.
let y = value in certificates of deposit.
you have two equations that need to be solved simultaneously.
they are:
x + y = 50,000
.17x + .07y = 6,000
the overall interest rate will be 12% because .12 * 50,000 = 6000.
this was just a check to make sure that the highest interest rate investment would be enough to cover her interest requirements.
it does.
multiply both sides of the first equation by .17 and leave the second equation as is to get:
.17x + .17y = 8500
.17x + .07y = 6000
subtract the second equation from the first to get:
.10y = 2500
solve for y to get:
y = 25000
looks like she should invest 25000 in b-rated bonds and 25000 in certificates of deposit.
original equations becomes:
x + y = 25000 + 25000 = 50,000
.17x + .07y = 4250 + 1750 = 6000.
your solution is she should invest 25000 in b-rated bonds paying 17% and 25000 in certificates of deposit paying 7% to get a total annual interest of 6000 from both.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The other tutor showed a good formal algebraic solution.
Note, however, that the numbers in this problem make for an easy mental solution.
$6000 return on an investment of $50,000 is a rate of 12%, which simple mental calculations show is exactly halfway between 7% and 17%. That means equal amounts need to be invested in the bonds and CDs.
ANSWER: $25,000 in bonds and $25,000 in CDs
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
x = amount invested in bonds
50000 - x = amount invested in the CD
0.17x + 0.07(50000 - x) = 6000
is the equation to form.
This is because,
0.17x = amount earned from the bonds
0.07*(50000-x) = amount earned from the bonds
this is over a 1 year time span
Let's solve for x.
0.17x + 0.07(50000 - x) = 6000
0.17x + 0.07(50000) + 0.07(-x) = 6000
0.17x + 3500 -0.07x = 6000
0.10x + 3500 = 6000
0.10x = 6000 - 3500
0.10x = 2500
x = 2500/0.10
x = $25,000 must be invested in bonds.
The other $25,000 would be invested in the CD.
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