algebra problem?
Assume that her total winnings are $ 400000, that the utility bonds will pay 4 percent per year, and that the savings account will pay 1 percent per year.
How much should she allocate to each investment in order for the yearly incomes from them to be the same?
Utility Bonds: $
Savings Account: $
What will be her total yearly income from these investments? $
Comments
Algebraically:
Let B = amount invested in bonds
Let S = amount invested in savings
We know that:
B + S = 400,000
0.04B = 0.01S
Take the bottom equation and multiply both sides by 100 to remove the decimals.
4B = S
Now substitute S = 4B into the first equation:
B + 4B = 400,000
5B = 400,000
B = 80,000
Then solve for S:
S = 4B = 4(80,000) = 320,000
So put $320,000 in savings and $80,000 in bonds.
The resulting income will be:
$320,000 x 0.01 = $3,200 from savings
$80,000 x 0.04 = $3,200 from bonds
Say the ulitity investment is x dollars
This make the saving investment 400,000 - x dollars
The utility interest will be 4 x/100 dollars and the saving interest will be (400000 -x) 1/100.
Equating and multiplying both side by 100
4x = 400000 -x which leads to x= 8,000
This the ultility investment is $80,000 and the saving investment is $320,000, Both will make $3,200 giving an income of $6,400
First year income:
.04(U) = .01(400000 - U)
.04U = 4000 - .01U
.05U = 4000
U = 80000
S = 400000 - 80000 = 320000
Y = .04(80000) + .01(320000) = 3200 + 3200 = 6400
This will remain constant, year to year, unless the interest is added back into the principal.
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