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PLEASE HELP
You invested $10,000 in two accounts paying 7% and 8% annual interest, respectively. If the total interest earned for the year was $780, how much was invested at each rate?
The amount invested at 7% is $0

PLEASE HELP You invested 10000 in two accounts paying 7 and 8 annual interest respectively If the total interest earned for the year was 780 how much was invest class=

Respuesta :

Using simple interest, it is found that:

  • The amount invested at 7% is $2,000.
  • The amount invested at 8% is $8,000.

Simple Interest

Simple interest is used when there is a single compounding per time period.

The interest after t years in is modeled by:

[tex]I(t) = Prt[/tex]

In which:

  • P is the initial amount.
  • r is the interest rate, as a decimal.

In this problem:

  • A total of $10,000 was invested, hence [tex]P_1 + P_2 = 10000[/tex].
  • Two accounts paying 7% and 8% annual interest, respectively, hence [tex]r_1 = 0.07, r_2 = 0.08[/tex].
  • The total interest earned for the year was $780, hence [tex]t = 1, I_1 + I_2 = 780[/tex]

Then:

[tex]I_1 = 0.07P_1[/tex]

[tex]I_2 = 0.08P_2[/tex]

Considering [tex]P_1 + P_2 = 10000 \rightarrow P_2 = 10000 - P_1[/tex]:

[tex]I_2 = 0.08(10000 - P_1)[/tex]

Considering [tex]I_1 + I_2 = 780 \rightarrow I_2 = 780 - I_1[/tex]:

[tex]780 - I_1 = 0.08(10000 - P_1)[/tex]

Considering [tex]I_1 = 0.07P_1[/tex]:

[tex]780 - I_1 = 0.08(10000 - P_1)[/tex]

[tex]780 - 0.07P_1 = 0.08(10000 - P_1)[/tex]

[tex]0.01P_1 = 20[/tex]

[tex]P_1 = \frac{20}{0.01}[/tex]

[tex]P_1 = 2000[/tex]

And:

[tex]P_1 + P_2 = 10000[/tex]

[tex]2000 + P_2 = 10000[/tex]

[tex]P_2 = 8000[/tex]

Then:

  • The amount invested at 7% is $2,000.
  • The amount invested at 8% is $8,000.

You can learn more about simple interest at https://brainly.com/question/25296782

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