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andreev551 [17]
3 years ago
15

A number cube is rolled 3 times.

Mathematics
1 answer:
Alex73 [517]3 years ago
3 0
6....................
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If $1,000 is invested at 4% simple interest, how much will the investment be worth after 2 years? Please explain how compound an
Novay_Z [31]
<h3>Answer:</h3>
  • simple interest: $1080.00
  • compounded annually: $1081.60
<h3>Step-by-step explanation:</h3>

<em>Simple Interest</em>

Simple interest is computed on the principal amount only. Each year, 4% of the principal is added to the balance. So, at the end of 2 years, the balance is ...

... $1000 + 0.04×$1000 + 0.04×$1000

... = $1000×(1 + 0.04×2) = $1000×1.08

... = $1080.00

_____

<em>Comment on the computation</em>

The added interest is the rate (per year) multiplied by the number of years. Here, that is 0.04×2×(principal amount). The formula for the simple interest earned is often seen as ...

... I = Prt . . . . . where I is the amount of interest, P is the principal amount, r is the interest rate for the time period, t is the number of time periods.

The account balance (A) with interest added is ...

... A = P + I = P + Prt

... A = P(1 +rt)

Here, the time period is years, and the rate given is an annual rate.

____

<em>Compound Interest</em>

Compound interest is computed on the <em>account balance</em> at the beginning of the period, not just the <em>principal</em> amount. After the first period, the account balance includes interest earned so far. So, the interest is earning interest. That is why it is called compounded interest.

Here, the balance at the end of the first year is the principal amount plus the interest that has earned:

... $1000 + 0.04×$1000 = $1000×1.04 = $1040.00

The balance at the end of the second year when the interest is compounded is this account balance plus the interest it earns:

... $1040 + 0.04×$1040 = $1040×1.04 = $1081.60

You may notice that the intial principal, $1000, has been multiplied by the factor 1.04 twice. Using exponents, the multiplier for a period of 2 years is 1.04×1.04 = 1.04².

_____

<em>Comment on the computation</em>

The multiplier of the account balance each year is raised to a power that is the number of years. Here, the account balance at the end of 2 years is (1+0.04)² times the principal amount. A formula that is seen for this is ...

... A = P(1 +r)^t . . . . . where A is the final account balance, P is the principal amount, r is the interest rate for the time period, and t is the number of time periods.

7 0
3 years ago
The last customer of the day calls telling you they purchased 96 meters of fencing to fence in a
Lilit [14]

Answer:

Area = 733 m² (to the nearest meter)

Step-by-step explanation:

<u></u>

<u>Formulae</u>

  • Circumference of a circle = 2\pir
  • Area of a circle =  \pir²

      (where r is the radius of the circle)

<u>Find the radius</u>

circumference = 96 m

Using the circumference of a circle formula:

⇒  2\pir = 96

⇒  \pir = 96 ÷ 2 = 48

⇒  r = 48 ÷ \pi = 48/\pi

<u>Find the area</u>

radius r = 48/\pi

Using the area of a circle formula:

⇒  A = \pir²

⇒  A = \pi(48/\pi)²

⇒  A = 2304/\pi

⇒  A = 733.3859778...

⇒  A = 733 m² (to the nearest meter)

6 0
2 years ago
Which is equivalent to (-4)3
sveticcg [70]

Answer(-6)2

Step-by-step explanation:

6 0
3 years ago
Shala says that 94% of the colored sheet of paper she has are blue. What decimal portion of her paper is shaded blue?
mixer [17]

Answer:

0.94 of her paper is shaded blue.

Step-by-step explanation:

94% needs the % sign moved to the left 2 times and a decimal will be placed where you stop at, so 0.94.

4 0
3 years ago
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Emily predicted her car payment to be
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Answer:

5

Step-by-step explanation:

6 0
3 years ago
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