Expert: Robi Bhattacharjee - 12/8/2008

Question
QUESTION: Hello:

Can you determine the answers to the following question by using a simple calculation?

An investor invests $30,000 in two accounts, $10,000 in one account and $20,000 in the second account.
What interest rates must these two accounts earn if the total return is $1,200 or 4%, $1,200/$30,000 = 4%?

Answers: 2% and 5%
(2% X $10,000) + (5% X $20,000) = $200 + $1,000 = $1,200.

Try not to use an an algebra calculation or something that is too advanced if possible.

I thank you for reply.

ANSWER: Hey Kenneth,

This problem can be done in two ways. One way is guess and check, the other is algebra.

Could you please tell me if you want me to go into the algebra or not, but since you said no algebra, then the only way is to get a lucky guess on the answer.



I hope this helped,
Robi

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

QUESTION: Hello:  

Solve by using the algebra version if possible.

Thanks!

Answer
Hi Kenneth,

Note that I am assuming the interest rates have to be integers. If they don't have to be integers, then please do notify me.

10,000x/100 + 20000y/100 = 1200

This is where x and y are the interest rates. This is since the total interest earned adds up to 1200.

so 100x + 200y = 1200

so dividing by 100

x + 2y = 12.

So this means that 12-2y = x

so for y = 1, x = 10

for y = 2, x = 8

for y = 3, x = 6

for y = 4, x = 4

for y = 5, x = 2

since the interest rates cannot be 0, the solutions are,
either 2%,5% or 4%, 4% or 6%, 3% or 8%, 2%. Any one of these work.


I hope this helped,
Robi