Expert: Sherry Wallin - 9/7/2009

Question
QUESTION: Hello:

At simple interest, an investor divides $1000.00 into two accounts -- one account of  $200 earning 2%, the second account of $800 earning 5%.  His total return is 4.4%,  ($44/$1000).

He decides to add a third account with the same amount of money, $1000. What amounts must he take from either the $200 or $800 account, or from both, so that his total return for the three accounts is still 4.4%?

Try to determine the answer with a non-algebraic solution.


ANSWER: Kenneth there are at least a couple of solutions to this problem. The one obvious (to me) is to earn 4.4% on the second $1000. (You don't specify that the 2nd thousand needs to be at any particular percent). If I assume that a part is at 2% and the other is at 5%, then you could just double the amounts invested at 2% and at 5% since the 2nd thousand is double the investment. This means invest $400 at 2% and $1600 at 5%. This answers your question that he takes nothing from the first two accounts.

Math Prof

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

QUESTION: Hello Math Prof:

Excuse my error!  The third account is to earn 8%, but do not add another $1000.00. Just divide the $1000 already in the two accounts into thirds and in someway use 2%, 5% and 8% for a total return of 4.4%

I thank you for your follow-up reply.

Answer
Ok Kenneth this makes a bit more sense! Your teacher wants a non-algebraic solution. There is always the guess and check method. I thought about finding the LCM (least common multiple) but I just reduced the 5% invested amount by $600 and increased the 2% invested amount by $300 which left me with $300 to invest at 8%. .02(500 an increase of 300) + .05(500 a decrease of 600) + .08(300 an increase of 300) = $44 or 4.4%(1000). Another way to try to explain this is that 2 + 8 = 10 and 2(5) = 10 so I figured out how much to make at 2% and at 8% and kept in mind how much I would lose at 5% (which is half of 10%).

Math Prof