Please help with Simple Annual Interest two part question?

[ShawnSaturday]

"Pat invest a total of $3000. Part of the money was invested in a more market account that paid 10% simple annual interest, and the remainder of the money was invested in a fund that paid 8% simple annual interest. If the total interest earned at the end of the first year from these investment was $256, how much did pat invest at 10% and how much at 8%?"

 

[Deleted member 4993]

"Pat invest a total of $3000. Part of the money was invested in a more market account that paid 10% simple annual interest, and the remainder of the money was invested in a fund that paid 8% simple annual interest. If the total interest earned at the end of the first year from these investment was $256, how much did pat invest at 10% and how much at 8%?"

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Please share your work/thoughts about this assignment.

Start with naming variables and writing equations.

Since we need to "find" the invested at two different interest rates - we will name those first:

Amount invested at 10% rate = T

Pat invest a total of $3000

so Amount invested at 8% rate = 3000 - T

Now continue......

 

[ShawnSaturday]

based on the equation, we would solve for T:

.08=3000-T
...subtract 3000 from both sides

-3000+.08= -T
...divide -1 from both sides

Thus, T= 2,999.92. Is this going in the right direction so far? Hence, why would the equation be set-up as you wrote it?

Secondly, I'm not sure if I understand the problem correctly; if "T" is the time it takes to earn $256, its given that it takes one year - "the total interest earned at the end of the first year from these investment was $256," so why is are we solving for "T" ? This is unclear for me.

 

[Deleted member 4993]

based on the equation, we would solve for T:

.08=3000-T
...subtract 3000 from both sides

-3000+.08= -T
...divide -1 from both sides

Thus, T= 2,999.92. Is this going in the right direction so far? Hence, why would the equation be set-up as you wrote it?

Secondly, I'm not sure if I understand the problem correctly; if "T" is the time it takes to earn $256, its given that it takes one year - "the total interest earned at the end of the first year from these investment was $256," so why is are we solving for "T" ? This is unclear for me.

you wrote:

-3000+.08= -T.................................Incorrect

How did you get that? What statement in the problem justifies that?

 

[ShawnSaturday]

you wrote:

-3000+.08= -T.................................Incorrect

How did you get that? What statement in the problem justifies that?

here is what I understand:

the total invested is $3000, which is the total of x and y amount combined. "x" is invested at 10% interest within 1 year and "y" is invested at 8% interest also within 1 year. The total earned interest is $256 combined from both x and y amount with interest of 10 and 8 percent or a total of 18% of the $3000.

> so, can the problem be broken down into two parts:

> 10% or .1x = 3000 + 1 -> determines "x" amount

> and 8% or .08y = 3000 + 1 -> determines, "y" amount

> "x" amount multiply by 10% interest and "y" amount multiply by 8% interest should sum up to $256.

> am I on the right track?

 

[firemath]

here is what I understand:

the total invested is $3000, which is the total of x and y amount combined. "x" is invested at 10% interest within 1 year and "y" is invested at 8% interest also within 1 year. The total earned interest is $256 combined from both x and y amount with interest of 10 and 8 percent or a total of 18% of the $3000.

> so, can the problem be broken down into two parts:

> 10% or .1x = 3000 + 1 -> determines "x" amount

> and 8% or .08y = 3000 + 1 -> determines, "y" amount

> "x" amount multiply by 10% interest and "y" amount multiply by 8% interest should sum up to $256.

> am I on the right track?

Create a graph.

 

[ShawnSaturday]

Create a graph.

what do you mean "create a graph" ???

 

[lev888]

the total invested is $3000, which is the total of x and y
> "x" amount multiply by 10% interest and "y" amount multiply by 8% interest should sum up to $256.

Can you come up with 2 equations based on the 2 statements above?

 

[Deleted member 4993]

"Pat invest a total of $3000. Part of the money was invested in a more market account that paid 10% simple annual interest, and the remainder of the money was invested in a fund that paid 8% simple annual interest. If the total interest earned at the end of the first year from these investment was $256, how much did pat invest at 10% and how much at 8%?"

I'll do a different but similar problem:

"Pat invest a total of $5000. Part of the money was invested in a more market account that paid 10% simple annual interest, and the remainder of the money was invested in a fund that paid 6% simple annual interest. If the total interest earned at the end of the first year from these investment was $400, how much did pat invest at 10% and how much at 6%?"

Amount invested at 10% rate = T

Pat invest a total of $5000

so Amount invested at 6% rate = 5000 - T

After one year Interest earned at 10% rate = T * (10/100)

After one year Interest earned at 6% rate = (5000 - T) * (6/100)

After one year TOTAL Interest earned at = T * (10/100) + (5000 - T) * (6/100)

Then

400 = T * (10/100) + (5000 - T) * (6/100)

400 = T * (10/100) + 300 - T * (6/100)

100 = T/25

T = 2500

So

Amount invested at 10% rate = 2500

Amount invested at 6% rate = 5000 - 2500 = 2500

 

[ShawnSaturday]

Thank you for showing me how to set the problem up. Following your example, this is what I calculated:

256 = T(.1) + (3000 - T).08
256 = .1T + 240 - .08T
16 = .02T
800 = T

So

Amount invested at 10% rate -> 2200
Amount invested at 8% rate -> 3000-2200 = 800

Based on the answer sheet, the amounts are correct. Please explain the logic behind the set-up so I will not get stomp the next time around?

Thanks again!

 

[Deleted member 4993]

Thank you for showing me how to set the problem up. Following your example, this is what I calculated:

256 = T(.1) + (3000 - T).08
256 = .1T + 240 - .08T
16 = .02T
800 = T

So

Amount invested at 10% rate -> 2200
Amount invested at 8% rate -> 3000-2200 = 800

Based on the answer sheet, the amounts are correct. Please explain the logic behind the set-up so I will not get stomp the next time around?

Thanks again!

Look at response #9.

At EXACTLY which line (calculation) you do not comprehend the logic?

 

[Deleted member 4993]

Thank you for showing me how to set the problem up. Following your example, this is what I calculated:

256 = T(.1) + (3000 - T).08
256 = .1T + 240 - .08T
16 = .02T
800 = T

So

Amount invested at 10% rate -> 2200
Amount invested at 8% rate -> 3000-2200 = 800

Based on the answer sheet, the amounts are correct. Please explain the logic behind the set-up so I will not get stomp the next time around?

Thanks again!

Please check your answer sheet again - very carefully. Your answers are NOT correct!