Interest Problem: how much should be invested so...?

[SCSmith]

An investment club invested $13,600 into two wimple interest accounts. On one account, the annual simple interest rate is 4.2%. On the other, the annual simple interest rate is 6%. How much should be invested in each account so that both accounts earn the same annual interest?


|=========|============|=======|================== =|
| | P | r | I |
|=========|============|=======|================== =|
| acct #1 | x | 0.042 | 0.042x |
|---------|------------|-------|-------------------|
| acct #2 | 13,600 - x | 0.06 | 0.006(13,600 - x) |
|=========|============|=======|================== =|
0.042x + 0.06(13,600 - x) = $27,200

0.042x + 816 - 0.06x = 27,200

0.036x = 26,834

x =

[stapel]

Your equation says that you expect the interest to sum to twice the originally-invested amount. Are you sure this is what you want?

Eliz.

[SCSmith]

The only other equation I can think of at this time is:

.042x=.006(13,600 - x)
.042x = 816 - .006x
.048x = 816
x = 17000

[Mrspi]

The only other equation I can think of at this time is:

.042x=.006(13,600 - x)
.042x = 816 - .006x
.048x = 816
x = 17000

Obviously, you've got an error here, since there's only $13,600 to be invested.

However, your idea for how to set up the equation is correct; each of the accounts are supposed to earn the same amount of interest. Your error is in using 0.006 for the interest rate on the right-hand side. In the chart you displayed in your original post, you correctly used 0.06:

.042x = .06(13600 - x)

Try this equation, and see if you get a more reasonable answer! Then, CHECK your answer to see if both accounts will earn the same amount of interest.

[SCSmith]

I don't see another way to set up the equation.

.006(13,600 -x) = .042x
81.6 - .006x = .042x
81.6 = .048x
1700 = x

[stapel]

As suggested by the earlier reply, you might want to reconsider using "0.006" for "six percent".

Eliz.

[Denis]

I don't see another way to set up the equation.
.006(13,600 -x) = .042x

Smitty, do you take the time to READ replies?
You were told that .006 is WRONG and should be .06; are you tired or something?

[SCSmith]

.042(13600)=.06(13600-x)
571.20=816-.06x
-244.80=-.06x
x=4080
13600-4080=9520

Correct answer is 4.2%=$8000 and 6%=$5,600

[Denis]

.042(13600)=.06(13600-x)

WHY did you change .042x to .042(13600) ? :evil: