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3 years ago

Sean invests $10,000 at an annual rate of 5% compounded continuously, according to the

Mathematics

1 answer:

tatiyna3 years ago

7 0

Answer:

if you have a pic of question send it plz then will give answer

Step-by-step explanation:

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Lauren will make annual contributions in the amount of $4,770, on average, to a 401(k) over the next 34 years. Her employer will

fredd [130]

Answer:

$610,297.11

Step-by-step explanation:

The problem seems to make several assumptions:

contributions are made at the end of each year
contributions and employer matching funds are not taxed until retirement
the 15% tax rate applies to the account balance amount at retirement

Of these, the last is least likely to be true in the United States.

___

Based on the assumptions above, we compute the amount from the future value of the series of contributions, then subtract 15% from that result.

FV = P·((1 +r)^n -1)/r . . . . where P is the amount of each payment, r is the annual interest rate, n is the number of payments.

The amount deposited each year is ...

$4770 + 0.60·4770 = $7630

Then the future value after 34 deposits is ...

FV = 7630·(1.055^34 -1)/0.055 ≈ 717,996.60

When this amount is reduced by the assumed 15% tax rate, it becomes ...

$717,996.60 - 0.15·717,996.60 = $610,297.11

4 0

3 years ago

Find the equation of the line passing through point (-1, -2) and having <br> slope 1/5. Show work.

STatiana [176]

Answer:

Y=1/5x+ -2

Step-by-step explanation:

Hope this helps

6 0

2 years ago

A circular swimming pool has a diameter of 40 meters. The depth of the pool is constant along west-east lines and increases line

Nataliya [291]

Answer:

Volume is $2000\pi\ m^{3}$

Solution:

As per the question:

Diameter, d = 40 m

Radius, r = 20 m

Now,

From north to south, we consider this vertical distance as 'y' and height, h varies linearly as a function of y:

iff

h(y) = cy + d

Then

when y = 1 m

h(- 20) = 1 m

1 = c.(- 20) + d = - 20c + d (1)

when y = 9 m

h(20) = 9 m

9 = c.20 + d = 20c + d (2)

Adding eqn (1) and (2)

d = 5 m

Using d = 5 in eqn (2), we get:

$c = \frac{1}{5}$

Therefore,

$h(y) = \frac{1}{5}y + 5$

Now, the Volume of the pool is given by:

$V = \int h(y)dA$

where

A = $r\theta$

$A = rdr\ d\theta$

Thus

$V = \int (\frac{1}{5}y + 5)dA$

$V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}rsin\theta + 5) rdr\ d\theta$

$V = \int_{0}^{2\pi}\int_{0}^{20} (\frac{1}{5}r^{2}sin\theta + 5r}) dr\ d\theta$

$V = \int_{0}^{2\pi} (\frac{1}{15}20^{3}sin\theta + 1000) d\theta$

$V = [- 533.33cos\theta + 1000\theta]_{0}^{2\pi}$

$V = 0 + 2\pi \times 1000 = 2000\pi\ m^{3}$

7 0

3 years ago

Give me a topic for my mathematical investigation.

Molodets [167]

There are a few you can choose from:

Statistics and probability

Geometry

Proofs

Triangles

Circles

Numerical sequences

Number Theory

etc.

6 0

3 years ago

Which expression is equivalent to 3√64k12?

jasenka [17]

The first one because when you simplify it equals to 3<span>√2x2x2x2x2x2xk12, so then you can take out two 2s and 4ks.

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3 0

3 years ago

Read 2 more answers