Suppose you want to start saving for retirement. You decide to continuously invest $5000 of your income each year in a risk-free investment with a 7% yearly interest rate compounded continuously. If y| is the value of the investment, and t| is in years. dy/dt =| Your answer should be interms of y|. You start investing at t = 0| so y(0) = 0. y(t) =| What is the size of your investment after 40 years. y(40) =|

Answers

Answer 1

Answer:

The size of the investment after 40 years is of $74,872.

Step-by-step explanation:

Continuous compounding:

The amount of money, in continuous compounding, after t years, is given by:

[tex]y(t) = y(0)(1+r)^t[/tex]

In which y(0) is the initial investment and r is the interest rate, as a decimal.

You decide to continuously invest $5000 of your income each year in a risk-free investment with a 7% yearly interest rate compounded continuously.

This means that [tex]y(0) = 5000, r = 0.07[/tex]. So

[tex]y(t) = y(0)(1+r)^t[/tex]

[tex]y(t) = 5000(1+0.07)^t[/tex]

[tex]y(t) = 5000(1.07)^t[/tex]

What is the size of your investment after 40 years?

This is y(40), that is, y when t = 40. So

[tex]y(t) = 5000(1.07)^t[/tex]

[tex]y(40) = 5000(1.07)^{40}[/tex]

[tex]y(40) = 74872[/tex]

The size of the investment after 40 years is of $74,872.


Related Questions

Find the volume. If you have any problems please tell me thank you.

Answers

Answer:

Step-by-step explanation:

Formula = V = l x w x h

V = 4.25 x 2.75 x 5

V = 58.438 --> 58.44

If 6x=48 find the value of 53-7x (A.) 5 (B) -3 (C) -5 (D) 3

Answers

Answer:

The answer is -3.

Step-by-step explanation:

If 6x=48, the answer for x is 8. And from there, I did 7(8). And then 53-56 and got -3.

The answer is B. -3.

Pls help me ASAP show work please

Answers

Answer:

$3.48 for each pair of socks.

Step-by-step explanation:

It's a little confusing, because it says they're buying 2 socks, but then asks for the price of each of 2 *pairs* of socks. I'm going to believe the first sentence should say they paid for 2 pairs of socks.

They have $10, and get $3.04 in change. So we'll subtract $3.04 from $10 to find out the cost of 2 pairs of socks.

10 - 3.04 = 6.96

Then divide $6.96 by 2 pairs of socks

6.96/2 = $3.48 for each pair of socks.

Will give Brainly plz answer fast

Answers

Answer:

sr for messy handwriting

Help&Show ur work plz<3

Answers

[tex]\huge{ \mathcal{  \underline{ Answer} \:  \:  ✓ }}[/tex]

The chords subtended by equal arcs are equal.

Therefore,

[tex]2x + 4 = 18[/tex]

[tex]2x = 14[/tex]

[tex]x = 7[/tex]

Hence, value of x = 7

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

chhering deposite rs. 40000 in a bank at the rate of 5% p.a. if he has to pay 5%of the total interest as tax for the bank how much will he get after 4 years​

Answers

Answer: Rs 7600

Step-by-step explanation:

The interest will be calculated as:

= Principal × Rate × Time

= 40000 × 5% × 4

= 40000 × 0.05 × 4

= 8000

Since he has to pay 5% of the total interest as tax for the bank, the amount that he will he get after 4 years will be:

= 8000 - (5% × 8000)

= 8000 - (0.05 × 8000)

= 8000 - 400

= 7600

Therefore, he'll get Rs 7600

Can someone help me with think fast?

Answers

Answer:

124

Step-by-step explanation:

A supplementary angle is 180

180-56=124

124 is the answer hope this helps

Find the sum of the geometric series if n = 6, r= 1/4, a = 2.

Answers

Sn = a(1-r^n)/(1-r)

Sn= 2(1-1/4096)/0.75= 2.67

PLS HELP THIS IS A TEST

Which number satisfies the inequality below?

1.75x + 4.50 < 20

a: 13
b: 14
c: 9
d: 7

Answers

Answer:

D: 7

Step-by-step explanation:

1.75 (7) + 4.50

12.25 + 4.50

= 16.75

16.75 < 20

Write down the general equation of the normal distribution

Answers

The following is the plot of the normal percent point function. where \phi is the cumulative distribution function of the standard normal distribution and Φ is the probability density function of the standard normal distribution.

Warner was paid $375.25 for working 25 hours. What was his hourly pay?

Answers

Answer:

$15.01 an hour

Step-by-step explanation:

[tex]\frac{375.25}{25}=15.01[/tex]

Ivan and Tanya share £150 in the ratio 4 : 1
Work out how much more Ivan gets compared to Tanya.

Answers

Answer:

£90 more

Step-by-step explanation:

4+1=5

150/5=30

I:T

4:1 ×30

120:30

120-30=90

explain or not idc lol

Answers

Answer:

B, 20,000

Step-by-step explanation:

429 X 48 = 20,598

If you estimate, it would be 20,000.

So, there you know B, 20,000 is your answer.

Justin earns $75 per week . How much does he earn in 30 weeks

Answers

the answer is $2,250

Answer:

$2,250

Step-by-step explanation:

$75=1 week

$75×30=$2,250

The midpoint of the coordinates (9, 11) and (7,8) is​

Answers

Answer:

The midpoint: (8,9.5)

Step-by-step explanation:

((9+7)/2,(11+8)/2))

Help please!!!!!!!!!!!!!!!

Answers

Answer:

-1, 5

Step-by-step explanation:

no really explanation, but its a graph and when u have agraph x goes before y. and the x in the middle of it is what its talking about and u can see the middle is on a 5 and a -1

The figure shows a plane slicing through a cone. The plane is neither parallel nor perpendicular to the base of the cone, and the plane does not intersect the base of the cone.

Answers

Answer:   Ellipse

==================================================

Explanation:

Imagine that this plane was a saw blade, or a laser, that cut the cone. We would have two pieces and each piece would have a shape of an ellipse on them. The cutting plane would also have the same ellipse shape.

Or you think of the cutting plane as a flat piece of cloth. If we cut everything around the cone, then we would have an ellipse shaped hole as a result.

The reason why we get an ellipse and not a circle is because the plane is angled like that. It needs to be perfectly parallel to the circular base in order to get a circular cross section.

Please can somebody help me please!

Answers

Answer:

h = 12 ft

Step-by-step explanation:

Area of a rectangle formula:

A = bh

Given:

A = 24b

b = 2b

Work:

A = bh

24b = 2b(h)

h = (24b)/(2b)

h = 12

which of the following is equivalent to (5-7i)(5-7i)

Answers

Answer:

Step-by-step explanation:

Here we are multiplying together two complex numbers which happen to be identical:  both are 5 - 7i).

This is also "the square of 5 - 7i:  (5 - 7I)^2

In both cases, the result is 25 - 35i - 35i - 49, or 74 - 70i

Karen has calls has 500 or 900 yards of thick soft wool, she has 200 feet at the strore they have 500 feet of wool. How many balls should she buy

Answers

Answer:

Yes.

Step-by-step explanation:

Because yes.

You saved $200 on your new laptop because you bought it online. If this was a 20% savings from the original price, find the original cost of the lapto

Answers

Answer:

$1000

Step-by-step explanation:

$200 was saved on a new laptop

This was 20% of the original price of the laptop

Therefote the original cost of the laptop can be calculated as follows

= 20/100x = 200

= 0.2x= 200

Divide both sides by the coefficient of x which is 0.2

x= 200/0.2

= 1000

Hence the original cost of the laptop is $1000

Just Ignore Q5 if you don’t know so plz don’t answer plz give me the answer of Q3 fast fast

Answers

x= 59. 68+2x+4=180. Combine like terms (68 and 4) 72+2x=180 subtract 180-72=118 then divide by two to get x. If it’s wrong my bad

Answer:

2x + 4 = 6x

68 = 6x

6 6

11.33

11.3 = x

Angle 3 and angle 8 are corresponding. So we firstly find 2x + 4 which is 6x

Since we are looking for x we divide 68 from 6 which gives u 11.3

I have 225 in my account I can spend all but 20%

Answers

Answer:

20 % is 45 so keep this much remaining

Step-by-step explanation:

Answer:

You can spend 80%. Multiple 225 × 0

80. 225×0.80 = 180. Now you will have $180

Step-by-step explanation:

Have a great day and summer.

92.6% of 738 toy robots on an assembly line will be approved by the quality-control inspector. Write and solve a proportion to find how many robots will be approved.

Answers

Answer: D. n/738 = 92.6/100 ;683 robots

Explantion: cross multiply 738 x 92.6 then divide by 100

Write an explicit formula for an, the nth term of the sequence 1, 11, 21

Answers

Answer:

an = 10n - 9.

Step-by-step explanation:

This is arithmetic with first term a1 = 1 and common difference 10.

an = a1 + d(n-1)

= 1 + 10(n - 1)

= 1 + 10n - 10

= 10n - 9.

The length of a rectangle is 4 inches less than twice its width. If the perimeter of the rectangle is 64 inches, what are the dimensions of the rectangle?

Show work please

Answers

Answer:

Step-by-step explanation:

=
3x-2
6
which of the following is the inverse of f(x)?
2x-3
6
O A. f-'(x) = 2x
O f-
B. F'(x) = 6452
O C. F'(x) = 6*+2
O D. F'(x) = 2***

Answers

Answer:

i thi nk correct answer is b so

An automobile insurance company divides customers into three risk categories: Good (G), Medium (M), and Poor (P). Assume the following distribution of customers: 70% are Good risks, 20% are Medium risks, and 10% are Poor risks. Assume that the probabilities of a customer filing an accident claim (C) in the course of a year are: 0.5% for Good, 1% for Medium, and 2.5% for Poor. A customer is chosen at random.
a) What is the probability that the customer is a good risk and has filed a claim?b) What is the probability that the customer has filed a claim?c) Given that the customer has filed a claim, what is the probability that the customer is a good risk?

Answers

Answer:

a) 0.035 = 3.5% probability that a customer is a good risk and has filed a claim.

b) 0.0395 = 3.95% probability that the customer has filed a claim.

c) 0.8861 = 88.61% probability that the customer is a good risk

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that the customer is a good risk and has filed a claim?

70% are good risks.

Of those, 0.5% file a claim. So

[tex]0.7*0.05 = 0.035[/tex]

0.035 = 3.5% probability that a customer is a good risk and has filed a claim.

b) What is the probability that the customer has filed a claim?

0.5% of 70%(good risks)

1% of 20%(medium risks)

2.5% of 10%(poor risks). So

[tex]0.05*0.7 + 0.01*0.2 + 0.025*0.1 = 0.0395[/tex]

0.0395 = 3.95% probability that the customer has filed a claim.

c) Given that the customer has filed a claim, what is the probability that the customer is a good risk?

0.0395 = 3.95% probability that the customer has filed a claim means that [tex]P(A) = 0.0395[/tex]

0.035 = 3.5% probability that a customer is a good risk and has filed a claim means that [tex]P(A \cap B) = 0.035[/tex]

Thus

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035}{0.0395} = 0.8861[/tex]

0.8861 = 88.61% probability that the customer is a good risk

You determined that you can make 72 donuts in 2hours. At rate,how many donuts can you make in 8 hours?

Answers

Answer:

288 donuts

Step-by-step explanation:

Answer:

288 donuts

Step-by-step explanation:

72 divided by 2 is 36 so that means you will make 36 donuts in 1 hour so now we have our unit rate which is 36. so then you multiply 36 by 8 and you get 288. that is your answer

The cost of 3 pounds of grapes is $9.75. What is the constant of proportionality that relates the cost in dollars, y, to the number of pounds of grapes, x? pls help, its due by the end of the day (3 pm)

Answers

Answer:

3.75

Step-by-step explanation:

We can write a ratio to solve

3 lbs             x lbs

---------- = -----------

9.75            y dollars

Using cross products

3y = 9.75 x

Divide each side by 3

3y/3 = 9.75x/3

y =3.75x

The constant is 3.75

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