Expert: Sherry Wallin - 11/20/2008

Question
QUESTION: Hello:

Can you solve the following by using a weighted average calculation?

An investor has $30,000 to invest at simple interest for one year. One portion at 2% and the other portion at 5%.
What amounts must be invested at these percentages if the total return is 4% or $1,200?

Answers: $20,000 and $10,000


I thank you for your reply.

ANSWER: I'm not sure what you are wanting to know. Are you wanting to know if the problem can be solved using weighted averages or if I can use weighted averages to solve the problem? All the information is here:

take the amount invested at 2% which is 10,000 and multiply it by .02
likewise take the amount invested at 5% which is 20,000 and multiply it by .05

.02(10000) + .05(20000) = 200 + 1000 = 1200
now divide the 1200 by the total amount of the investment
1200/30000 = .04 or 4% which is the weighted average interest paid
check .04(30000) = 1200

Again I'm not sure what you are trying to do because all the information is given.

Or are you wanting to know how these values were arrived at, i.e., how the $10,000 and $20,000 were found?

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply.

I want to know how to these values, that is, how the $10,000 and $20,000 were found, by using a weighted average.

I thank you for your follow-up reply.

Answer
I tell my students to set up a table of values and to label the variable
let x = amount invested at 2% and 30,000-x is the amount invested at 5%

amount          rate          value
x          .02          .02x
30,000-x          .05          .05(30,000-x)
______________________________________________________________
30,000          .02x + .05(30,000-x)= 1200
multiply by 100          2x + 5*30,000 -5x = 120,000
(gets rid of decimals)          -3x + 150,000 = 120,000
         30,000 = 3x
         x = 10,000

x = 10,000 is the amount invested at 2% and 30,000-10,000 = 20,000 is the amount invested at 5%

Note that 10,000/30,000 = 1/3 and 20,000/30,000 = 2/3 these are the weights
(1/3)(.02) + (2/3)(.05) = .12/3 = .04 = 4%
(you may prefer to think of 1/3 as .33 and 2/3 as .67
then you have .33(.02) + .67(.05) = .04 = 4% also

Hopefully this answers the question for you :)

Math Prof