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pashok25 [27]
3 years ago
5

  Sarah Wiggum would like to make a single investment and have ​$1.7 million at the time of her retirement in 34 years. She has

found a mutual fund that will earn 7 percent annually. How much will Sarah have to invest​ today
Mathematics
1 answer:
vovangra [49]3 years ago
8 0

Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

T = E + P

In this question:

t = 35, I = 0.07, T = 1700000

She has to invest P today.

T = E + P

1700000 = E + P

E = 1700000 - P

So

E = P*I*t

1700000 - P = P*0.07*34

3.38P = 1700000

P = \frac{1700000}{3.38}

P = 502958.58

Sarah has to invest $502,958.58 today.

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The money in the Felix's account will be $6798 when he is 21.

<u>Step-by-step explanation:</u>

It is given that,

  • The amount deposited is $2000.
  • The account earns 6%  compound interest.
  • It is compounded  annually for 21 years.

<u>To find the money in Felix's account after 21 years :</u>

The formula used here is,

⇒ A = P(1+r/n)^{nt}

where A is the amount after 21 years.

  • P is the initial amount deposited ⇒ P = 2000
  • r is the rate ⇒ r = 0.06
  • n is the number of times interest is compounded per year⇒ n = 1
  • t is the time period ⇒ t = 21

⇒ 2000(1+0.06/1)^{21\times 1}

⇒ 2000(1.06)^{21}

⇒ 2000\times3.399

⇒ 6798

Therefore, The money in the Felix's account will be $6798 when he is 21.

4 0
3 years ago
The curve with equation y=ax^2+bx has a gradient of 3 at the point (2,-2). Find the values of a and b.
Airida [17]

Answer:

a = 2, b = - 5

Step-by-step explanation:

Given

y = ax² + bx

\frac{dy}{dx} is the measure of the slope at x = a

Differentiate each term with respect to x using the power rule

\frac{d}{dx}(ax^{n} ) = nax^{n-1}

\frac{dy}{dx} = 2ax + b, hence

2ax + b = 3 at (2, - 2)

Substitute x = 2 into \frac{dy}{dx}

4a + b = 3 → (1) and substitute x = 2 into y

4a + 2b = - 2 → (2)

Subtract ( 1) from (2)

b = - 2 - 3 = - 5

Substitute b = - 5 into (1)

4a - 5 = 3 ( add 5 to both sides )

4a = 8 ( divide both sides by 4 )

a = 2

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Vsevolod [243]

Answer:

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Step-by-step explanation:

The percentage change is ...

  percentage change = (amount of change)/(original amount) × 100%

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Answer:

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