This is not a homework question! I am just curious to know how to solve this with a somewhat simple calculation.
Is there a method that can determine the answers to my questions by using a weighted average or some probability calculation?
(A) 5% X $2000 = $100
(B) 2% X $1000 = $20
This is a total return or an average of $120/$3000 = 4%
If I want to have an average or total return of 3%, what amounts must be in the A account and what dollar amount must be in the B account?
And also what percentage must the A and B accounts be changed to so that the average or total return is 3% but keep the dollar amounts in each account, A $2000 and B $1000, the same?
I know that this question is not directly related to probability and statistics, but perhaps you may offer some helpful solution.
I thank you for your reply
ANSWER: kenneth -
your question involves simple algebra and is not really a
probability question.
having said that, one could interpret your first question
as asking "what weighted average of 2% and 5% gives 3%?".
if the weights are w and 1-w, respectively (here w is a weight
between 0 and 1) you want to solve for w in
5w + 2(1-w) = 3.
this is a simple algebraic equation whose solution is w = 1/3.
so you put 1/3 of your money at 5% and the other 2/3 at 2% and you get
an average return of 3%.
if you have $3000, put $1000 at 5% and $2000 at 2%.
your second question does not have a unique answer. for example,
you could put $2000 at 4% and $1000 at 1% to get a 3% return. you
could also put the $2000 at 3.5% and the $1000 at 2% and get a 3%
return.
the formal solution to this question is this: let x and y be the
percentage yields for the $2000 and $1000 respectively. then you
want
(2000x + 1000y)/3000 = 3,
which simplifies to 2x + y = 9.
this is one equation in two unknowns (x and y) and has more than one
solution (for which neither x nor y are negative). in fact, it has
an infinite number of solutions. just pick a value for y, say, like
y = 1% and solve for x to get x = 4%. if you take y = 2%, you get
x = 3.5%. you could also take y = 0% and get x = 4.5%; and so on.
(you can't take y to be greater than 3%, however - since the formal
solution would then involve x being negative.)
ronny
---------- FOLLOW-UP ----------
QUESTION: Hello:
I want to thank you for the reply.
This appears to be a strange example. In 5% X $2000 = $100 and 2% X $1000 = $20, the $3000 is divided into thirds. This is a 4% total return, $120/$3000
Now, if the amounts are switched, the $1000 earns 5% and the $2000 earns 2%, the total return is 3%, $90/$3000, but the $3000 is still divided into thirds with the second example having a one percentage point difference.
I thank you for any reply that you may want to send.
Answer kenneth -
there are lots of curious phenomena that one encounters in the realm of
mathematics.
for example: the divisors of 28 are 1, 2, 4, 7 & 14. if you sum them,
they add up to 28. such numbers (which are the sum of their divisors)
are called perfect numbers.
there are many such - including one that is smaller than 28. can you
figure out what that smaller perfect number is?
