Simple Interest for two investments

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Homework Help Overview

The problem involves calculating the amounts invested by Pat in two different accounts with simple interest rates: one at 10% and the other at 8%. The total investment is $3000, and the total interest earned after one year is $256. Participants are exploring how to set up equations based on these conditions.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss setting up equations to represent the total investment and the interest earned. Some question the formulation of the equations and the distinction between total value and interest earned. Others suggest corrections to the original equations and variable names for clarity.

Discussion Status

There is ongoing exploration of the problem with various participants providing feedback and corrections. Some participants have offered guidance on how to properly distinguish between different variables and the importance of maintaining clarity in the equations. Multiple interpretations of the problem are being considered.

Contextual Notes

Participants note that there are four unknowns and four equations involved, and there is some confusion regarding the mixing of principal amounts and interest calculations. A typo in the calculations has been pointed out, affecting the interpretation of the results.

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Homework Statement


Pat invested a total of 3000$. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the interest earned at the end of first year from these investments was 256$, how much did Pat invest at 10 percent and how much at 8 percent?[/B]

Homework Equations


V = P(1 + rt/100)
V= interest amount
P = Principal amount
r = rate
t = time in years

The Attempt at a Solution


P = TenP + EightP or 3000 = TenP + EightP[/B]
V= TenV + EightV or 256 = TenV + EightV
For 10%
TenV = TenP ( 1 + 0.1 *1)
For 8%
EightV = EightP(1 + 0.08 *1)
I have not developed the full solution but is it fine to work in this way or there is any other possibility? Some body please guide me.

Zulfi.
 
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So far, so good. Keep going.

EDIT: See @scottdave 's correction regarding the equations for V, TenV, and EightV.
 
Last edited:
In your formulas: V = P(1 + rt/100), will give you the total Value (Principal plus Interest) at the end of the time period. If you want to find the interest earned, then you should use I = P*(rt/100). For example, if you invest 100 at 10% per year, at the end of the first year, you have V = $100(1 + (10)(1)/100) = $110. You started with $100 and end with $110, so you earn $10 (the interest).

In your situation, V equals the total at the end which is 3000 that you started with plus 256 interest = 3256.
 
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zak100 said:

Homework Statement


Pat invested a total of 3000$. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the interest earned at the end of first year from these investments was 256$, how much did Pat invest at 10 percent and how much at 8 percent?[/B]

Homework Equations


V = P(1 + rt/100)
V= interest amount
P = Principal amount
r = rate
t = time in years

The Attempt at a Solution


P = TenP + EightP or 3000 = TenP + EightP
V= TenV + EightV or 256 = TenV + EightV
For 10%
TenV = TenP ( 1 + 0.1 *1)
For 8%
EightV = EightP(1 + 0.08 *1)
I have not developed the full solution but is it fine to work in this way or there is any other possibility? Some body please guide me.[/B]

Zulfi.

I suggest you try to solve your two equations for the two variables TenP and EightP, to see what happens. That will show you how badly wrong is your formulation! You need to distinguish between the "interest earned" and the (total) "future value"---they are different, and you have mixed them up.
 
Last edited:
Hi,
I think its solvable. There are 4 unknowns and 4 equations. Mixing is possible because question has mixed 8% Principal with 10% Principal in the amount of 3000$ and then mixed their profits also. My answer is not corect.
P = TenP = EightP
3000 = TenP + EightP
Let x1= TenP and x2 = EightP
Now V= TenV + EightV
3256 = TenV + EightV
Let y1=TenV and y2 = EightV

Thank scottdave for his advice on this.

Now 3000 = x1 + x2---- (1)
and 3256 = y1 + y2-----(2)

We have
V = P(1 + rt/100)
For 10%
y1 = x1(1+0.1)
y1 = 1.1x1---(3)

For 8%
y2 = x2(1+0.08)
y2 = 1.08x2-----(4)

Putting y1 & y2 values from (3) and (4) into (2)

3256 = 1.1x1 + 1.082x2 ----(5)
Multiplying (1) by 1.1

3300 = 1.1x1 + 1.1x2 ----(6)

Subtracting (5) from (6)

3300 = 1.1x1 + 1.1x2
-3256 = -1.1x1 -1.082
_____________________

44 = 0.0182x2
x2= 2444

Therefore EightP = 2444

Putting x2 in (1)
3000 = x1 + 2444
TenP = x1= 556

Whats wrong with my solution? Some body please guide me.

Zulfi.
 
zak100 said:
Hi,
I think its solvable. There are 4 unknowns and 4 equations. Mixing is possible because question has mixed 8% Principal with 10% Principal in the amount of 3000$ and then mixed their profits also. My answer is not corect.
P = TenP = EightP
3000 = TenP + EightP
Let x1= TenP and x2 = EightP
Now V= TenV + EightV
3256 = TenV + EightV
Let y1=TenV and y2 = EightV

Thank scottdave for his advice on this.

Now 3000 = x1 + x2---- (1)
and 3256 = y1 + y2-----(2)

We have
V = P(1 + rt/100)
For 10%
y1 = x1(1+0.1)
y1 = 1.1x1---(3)

For 8%
y2 = x2(1+0.08)
y2 = 1.08x2-----(4)

Putting y1 & y2 values from (3) and (4) into (2)

3256 = 1.1x1 + 1.082x2 ----(5)
Multiplying (1) by 1.1

3300 = 1.1x1 + 1.1x2 ----(6)

Subtracting (5) from (6)

3300 = 1.1x1 + 1.1x2
-3256 = -1.1x1 -1.082
_____________________

44 = 0.0182x2
x2= 2444

Therefore EightP = 2444

Putting x2 in (1)
3000 = x1 + 2444
TenP = x1= 556

Whats wrong with my solution? Some body please guide me.

Zulfi.
Mainly you have a typo.

You changed $256 to 3256 throughout.
 
zak100 said:
Hi,
I think its solvable. There are 4 unknowns and 4 equations. Mixing is possible because question has mixed 8% Principal with 10% Principal in the amount of 3000$ and then mixed their profits also. My answer is not corect.
P = TenP = EightP
3000 = TenP + EightP
Let x1= TenP and x2 = EightP
Now V= TenV + EightV
3256 = TenV + EightV
Let y1=TenV and y2 = EightV

Thank scottdave for his advice on this.

Now 3000 = x1 + x2---- (1)
and 3256 = y1 + y2-----(2)

We have
V = P(1 + rt/100)
For 10%
y1 = x1(1+0.1)
y1 = 1.1x1---(3)

For 8%
y2 = x2(1+0.08)
y2 = 1.08x2-----(4)

Putting y1 & y2 values from (3) and (4) into (2)

3256 = 1.1x1 + 1.082x2 ----(5)
Multiplying (1) by 1.1

3300 = 1.1x1 + 1.1x2 ----(6)

Subtracting (5) from (6)

3300 = 1.1x1 + 1.1x2
-3256 = -1.1x1 -1.082
_____________________

44 = 0.0182x2
x2= 2444

Therefore EightP = 2444

Putting x2 in (1)
3000 = x1 + 2444
TenP = x1= 556

Whats wrong with my solution? Some body please guide me.

Zulfi.

Where did your figure of 1.082 come from? How did 1.08 x2 become 1.082 x2? How did 1.1 - 1.08 become 0.0182?

CHECK YOUR WORK BEFORE ASKING QUESTIONS HERE!
 
In many problems, the hardest job is to keep the meaning of all the variables straight.
Your switch from somewhat meaningful variable names like TenP to unrecognizable names like x and y does not help to keep things straight. With your new x and y variables, I got tired of trying to understand what you are doing. I recommend using a letter that indicates interest, like 'I' rather than 'V'. Rename V to I, TenV to TenI, and EightV to EightI.

Have you corrected the equations for V, TenV, EightV as @scottdave recommended? You must correct that.
 
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When you say this:
zak100 said:
Subtracting (5) from (6)

3300 = 1.1x1 + 1.1x2
-3256 = -1.1x1 -1.082
_____________________

44 = 0.0182x2
x2= 2444
You have a typo.
It really should be:

3300 = 1.1x1 + 1.1x2
-3256 = -1.1x1 -1.08x2
----------------------------
44 = 0.02x2

x2= 2200

Then continue from there. I agree with @FactChecker that using more meaningful variable helps to keep things straight.
 
  • #10
Hi,
Thanks everybody.

Subtracting (5) from (6)

3300 = 1.1x1 + 1.1x2
-3256 = -1.1x1 -1.08x2
_____________________

44 = 0.02x2
x2= 2200

Therefore EightP = 2200

Putting x2 in (1)
3000 = x1 + 2200
TenP = x1= 800

Thanks scottdave for catching my error. This is the correct answer.

Zulfi.
 

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