Question 1159813: If you decide to make two investments that yield the same return, how much did you invest in each?
(1) Of the total amount invested, 3/10 of it plus $600,000.00 invested in the first one.
(2) At the end of the first year you received $150,000.00 in total return.
A) (1) on its own.
B) (2) on your own.
C) Both (1) and (2) together.
D) Each on its own, (1) or (2).
E) Additional information is required.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! as far as i can see, you probably need both 1 and 2 plus some additional information, like the interest rate.
my reasoning is as follows:
let x = the amount of the original investment.
first investment was 3/10 * x + 600,000
second investment would be 7/10 * x - 600,000.
the reason for this is the total investment has to be x, therefore:
3/10 * x + 600,000 + 7/10 * x - 600,000 = x.
if you let y equal the common interest rate, then the formula for the interest becomes:
(3/10 * x + 600,000) * y + (7/10 * x - 600,000) * y = 150,000
simplify to get:
3/10 * xy + 600,000 * y + 7/10 * xy - 600,000 * y = 150,000
combine like terms to get:
xy = 150,000
x is the original investment.
y is the interest rate.
you can't find the original investment because you don't know what the interest rate is.
for example:
assume the interest rate was 10%.
the formula would then become x * .10 = 150,000
you would then solve for x to get x = 150,000 / .10 = 1,500,000.
the first investment would be 3/10 * that + 600,000 = 1,050,000.
the second investment would be 7/10 * that - 600,000 = 450,000.
total investment would be 1,050,000 + 450,000 = 1,500,000.
interest for first investment would be 105,000.
interest for second investment would be 45,000.
total interest would be 105,000 + 45,000 = 150,000.
if you assumed an interest rate, then you could find the amount of the original investment.
without that, you're out of luck, because you don't have sufficient information.
that's what i'm thinking.
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