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3 years ago

8

how much must you deposit in an account that pays 8% annual interest compounded monthly to have a balance of $1,000 after one ye

ar

1 answer:

strojnjashka [21]3 years ago

5 0

Answer:

$\$923.36$

Step-by-step explanation:

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=1\ year\\ A=\$1,000\\ r=0.08\\n=12$

substitute in the formula above and solve for P

$\$1,000=P(1+\frac{0.08}{12})^{12*1}$

$P=\$1,000/(1+\frac{0.08}{12})^{12*1}=\$923.36$

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Colin walked a distance of 15 miles in 6 hours. <br> Work out out

butalik [34]

Answer:

Colin walked 2.5 miles every hour

Step-by-step explanation:

The answer is 2.5 because 15 divided by 6 is 2.5

P.S Can I have brainliest?

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2 years ago

jim walks at an average rate of 4 miles per hour. at this rate how long will it take jim to walk 10 miles?

Firdavs [7]

It would take him 2.5 hrs because when you divide 10 by 4 that's what you get

7 0

3 years ago

Read 2 more answers

A person is supposed to drink half a gallon of water every day.abby drank 15 small cups today if the capacity of the cup is 3.5

Yuki888 [10]

He needs to drink 3 cups MORE to meet his daily requirement.

Step-by-step explanation:

Here, as given in the question:

The total need for water = half a gallon = 0.5 gallon

1 gallon = 128 oz

So, 0.5 gallon = 128/2 = 64 oz

Now, the capacity of 1 cup = 3.5 oz

The number of cups already drank by the person = 15 cups

So, the total amount of water already taken by him

= 15 cups x Capacity of 1 cup

= 15 x (3.5 oz) = 52.5 oz

So, the amount of water left to be drink by him

= Total Need - Already covered

= 64 oz - 52 . 5 oz = 11.5 oz

Now, as 1 cup = 3.5 oz

So, 11.5 oz has $( \frac{11.5}{3.5} )$ cups = 3.28 cup≈ 3 cups

Hence, he needs to drink 3 cups MORE to meet his daily requirement.

6 0

3 years ago

Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio

JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

$\frac{dA}{dt} = kA$

Where k represents the constant of proportionality

$\frac{dA}{dt} = kA$

Multiply both sides by dt/A

$\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}$

$\frac{dA}{A} = k\ dt$

Integrate both sides

$\int\ {\frac{dA}{A} = \int\ {k\ dt}$

$ln\ A = kt + lnC$

Make A, the subject

$A = Ce^{kt}$

$t = 0\ when\ A =1\ million$ i.e. At initial

So, we have:

$A = Ce^{kt}$

$1000000 = Ce^{k*0}$

$1000000 = Ce^{0}$

$1000000 = C*1$

$1000000 = C$

$C =1000000$

Substitute $C =1000000$ in $A = Ce^{kt}$

$A = 1000000e^{kt}$

To solve for k;

$6\ years\ later = 500,000$

i.e.

$t = 6\ A = 500000$

So:

$500000= 1000000e^{k*6}$

Divide both sides by 1000000

$0.5= e^{k*6}$

Take natural logarithm (ln) of both sides

$ln(0.5) = ln(e^{k*6})$

$ln(0.5) = k*6$

Solve for k

$k = \frac{ln(0.5)}{6}$

$k = \frac{-0.693}{6}$

$k = -0.1155$

Recall that:

$\frac{dA}{dt} = kA$

Where

$\frac{dA}{dt}$ = Rate

So, when

$A = 600000$

The rate is:

$\frac{dA}{dt} = -0.1155 * 600000$

$\frac{dA}{dt} = -69300$

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

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2 years ago

Find the product and fill in the blanks to write in standard complex number form

k0ka [10]

X^2 +2x +10 = 0

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x_1,2 = (-2 +/- sqrt(-36))/2 = (-2 +/- 6i)/2 = 2(-1 +/- 3i)/2 = -1 +/- 3i

x_1,2 = -1 +/- 3i or more understandably

x_1 = -1 -3i and x_2 = -1 +3i

hope this will help you

3 0

3 years ago