AboutPaul Klarreich Expertise I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
At simple interest, if an investor has $1000.00 to invest in multiple accounts at different percentages (See examples below.), and he wants a total return of 4%, is there one calculation that can be used to determine these amounts for these accounts?
For example:
Invest $1000.00 @ 2% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
etc.
I thank you for your reply
ANSWER: Questioner: Kenneth
Country: United States
Category: Advanced Math
Private: No
Subject: Interest
Question: Hello:
At simple interest, if an investor has $1000.00 to invest in multiple accounts at different percentages (See examples below.), and he wants a total return of 4%, is there one calculation that can be used to determine these amounts for these accounts?
For example:
A. Invest $1000.00 @ 2% and 5% for total return of 4%.
B. Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
C. Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
D. Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
etc.
I thank you for your reply
............................................
Hi, Kenneth,
Example A is a standard 'mixture/rate-time-distance/etc.' kind of problem with a unique solution. Just look in any elementary algebra book and you will find plenty of these.
Basically, let x = am't invested at 2%, then
1000-x = am't inv. at 5%.
Then 0.02x + 0.05(1000-x) = 1000(0.04)
and solve.
B,C,D have multiple solutions, and are obviously not well-defined. For example:
......................................
D. Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
Solution: Invest it all at 4%. (Duh....) And, naturally, there are other ways.
.......................................
B. Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Solution: Invest NONE of it at 2%. That reduces it to problem A, which has already been solved.
........................................
---------- FOLLOW-UP ----------
QUESTION: Hello:
I want to thank you for your reply. I have a follow-up question regarding D:
D. Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
Solution: Invest it all at 4%. (Duh....) And, naturally, there are other ways.
--------------------------
How is investing it all at 4% the same as investing $1000 in for separate accounts at 2%, 3%, 4%, and 5%?
I know that there is a one percentage point difference between these percentages, but I divided $1000.00 into
$400 @ 2%, $200 @ 3%, $300 @ 4%, and $100 @ 5% but the total return is not 4%. It is $31/$1000 = 3.1%.
I thank you for your reply.
Answer Questioner: Kenneth
Country: United States
Category: Advanced Math
Private: No
Subject: Interest
Question: QUESTION: Hello:
At simple interest, if an investor has $1000.00 to invest in multiple accounts at different percentages (See examples below.), and he wants a total return of 4%, is there one calculation that can be used to determine these amounts for these accounts?
For example:
Invest $1000.00 @ 2% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
etc.
I thank you for your reply
ANSWER: Questioner: Kenneth
Country: United States
Category: Advanced Math
Private: No
Subject: Interest
Question: Hello:
At simple interest, if an investor has $1000.00 to invest in multiple accounts at different percentages (See examples below.), and he wants a total return of 4%, is there one calculation that can be used to determine these amounts for these accounts?
For example:
A. Invest $1000.00 @ 2% and 5% for total return of 4%.
B. Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
C. Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
D. Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
etc.
I thank you for your reply
............................................
Hi, Kenneth,
Example A is a standard 'mixture/rate-time-distance/etc.' kind of problem with a unique solution. Just look in any elementary algebra book and you will find plenty of these.
Basically, let x = am't invested at 2%, then
1000-x = am't inv. at 5%.
Then 0.02x + 0.05(1000-x) = 1000(0.04)
and solve.
B,C,D have multiple solutions, and are obviously not well-defined. For example:
......................................
D. Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
Solution: Invest it all at 4%. (Duh....) And, naturally, there are other ways.
.......................................
B. Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Solution: Invest NONE of it at 2%. That reduces it to problem A, which has already been solved.
........................................
---------- FOLLOW-UP ----------
QUESTION: Hello:
I want to thank you for your reply. I have a follow-up question regarding D:
D. Invest $1000.00 @ 2%, 3%, 4%, and 5% for total return of 4%.
Solution: Invest it all at 4%. (Duh....) And, naturally, there are other ways.
--------------------------
How is investing it all at 4% the same as investing $1000 in for separate accounts at 2%, 3%, 4%, and 5%?
I know that there is a one percentage point difference between these percentages, but I divided $1000.00 into
$400 @ 2%, $200 @ 3%, $300 @ 4%, and $100 @ 5% but the total return is not 4%. It is $31/$1000 = 3.1%.
..........................................
Of course it isn't. What I meant was this:
If you try the same thing on D as we did on A, here is what happens:
Let x = am't invested at 2%
Let y = am't invested at 3%
Let z = am't invested at 4%
Then 1000 - (x + y + z) = am't inv at 5%.
Now you get ONE equation in THREE variables. It has an infinite number of solutions.
A similar thing happens with the others -- all except A.
Now if you want to talk about how you should do it to minimize risk, etc, you need to send it to the economics section.
