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matrenka [14]
1 year ago
14

Suppose you invest $5,000 at 4% annual interest. How much money would your investment be worth after 10 years? Round your answer

to the nearest hundredth (2 places after the decimal).
Mathematics
1 answer:
katrin2010 [14]1 year ago
4 0

The investment will be worth $7,401.22 after 10 years

Here, we want to calculate the amount the investment will be worth after 10 years

Mathematically, to get this, we will use the compound interest formula;

A\text{ = P(1 + }\frac{r}{n})^{nt}

where A is the amount after 10 years

P is the amount invested which is $5,000

r is the interest rate which is 4%, same as 4/100 = 0.04

n is the number of terms yearly the investment will be compounded. Since the interest rate is annual, then the number of times it will be compounded yearly is 1

t is the number of years which is 10 in this case

Substituting these values, we have;

\begin{gathered} A\text{ =5000 (1 + }\frac{0.04}{1})^{1\times10} \\  \\ A=5000(1+0.04)^{10} \\  \\ A=5000(1.04)^{10} \\  \\ A\text{ = 7,401.22} \end{gathered}

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Step-by-step explanation:

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3 years ago
An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the i
natita [175]

Answer:

  • $70,000 at 7%
  • $304,000 at 8%

Step-by-step explanation:

<u>Given</u>:

  Total interest earned on two investments is $29,220.

  An amount is invested at 7%.

  $24,000 more than 4 times that amount is invested at 8%.

<u>Find</u>:

  The amount invested at each rate.

<u>Solution</u>:

  Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

  interest on 7% account + interest on 8% account = total interest

  0.07x + 0.08(24000+4x) = 29220

  0.39x + 1920 = 29220 . . . . . . . . . . . simplify

  0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

  x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

  24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

<u><em>Check</em></u>

The answer must satisfy ...

  7% interest + 8% interest = 29,220

  0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

<em>Comment on 6-step method</em>

We have tried to hit the highlights. Your steps appear to be ...

  1. Identify the given information (Given)
  2. Identify the question you are asked to answer (Find)
  3. Identify the useless information in the problem statement (is none)
  4. Decide on a strategy. Make a model or drawing. (model equation shown)
  5. Solve and show work (Solution)
  6. Explain why the answer makes sense (Check)
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schepotkina [342]
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You can simplify this into 1/3 = .33
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faltersainse [42]

Answer:

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Step-by-step explanation:

4x = 7 - 8x - 27

1) Combine like terms (7 and -27). So, 7 + (-27) = -20.

        4x = 8x - 20

2) Subtract 8x from both sides of the equation. So, 4x - 8x = -4x.

        -4x = -20

3) Divide both sides by -4. So, -20 / -4 = 5.

        x = 5

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