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2 years ago

* Danny wants to earn $500,000 by the time he retires. He puts a huge bonus of $20,000 in an

Mathematics

1 answer:

zloy xaker [14]2 years ago

5 0

Answer:

See Below

Step-by-step explanation:

The question is asking:

After how many years, 20,000 will become 500,000 at an annual interest of 11.5%?

So, we need compound growth formula shown below to solve this:

$F=P(1+r)^t$

F is future value

P is present amount

r is rate of interest

t is the time of year

Given,

F = 500,000

P = 20,000

r = 11.5% = 11.5/100 = 0.115

t is what we want to find

$F=P(1+r)^t\\500,000=20,000(1+0.115)^t\\25=1.115^t$

Now, we take natural log of both sides and solve for t:

$Ln(25)=t*Ln(1.115)\\t=\frac{Ln(25)}{Ln(1.115)}\\t=29.57$

Its is going to take about 29.57 years, rounding, 30 years

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Your answer is correct actually

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Answer:

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3 years ago

What multiples to 42 and adds to -2

solniwko [45]

Answer:

Step-by-step explanation:

xy = 42

x+y = - 2 Substitute into the top equation

y = -2 - x Put in for y

x(-2 - x) = 42 Remove the brackets

-2x - x^2 = 42 Subtract 42 from both sides.

-2x - x^2 - 42 = 0 Put in the more normal order.

-x^2 - 2x - 42 = 0 Multiply by -1

x^2 + 2x + 42 = 0

This cannot be factored. It gives complex roots as it is written. I will give you the answer but I kind of doubt the question is correct.

x1 = - 1 + 6.40i

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Leave a comment if you have a correction.

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3 years ago

Caren is making rice and beans. She can spend no more than $10 on the ingredients. Which situation is represented by the inequal

sergij07 [2.7K]

If you are given $10 every 3.5 hours and you want to find the unit rate per hour, you want to solve for how much money you make every hour. You do this by dividing the $10 by the 3.5 hours, which will result in about $2.86 per hour. (This is a rounded value)

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2 years ago

In a G.P the difference between the 1st and 5th term is 150, and the difference between the

liubo4ka [24]

Answer:

Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

$a$ ,
$a\cdot r$ ,
$a \cdot r^2$ ,
$a \cdot r^3$ ,
$a \cdot r^4$ .

First equation:

$a\, r^4 - a = 150$ .

Second equation:

$a\, r^3 - a\, r = 48$ .

Rewrite and simplify the first equation.

$\begin{aligned}& a\, r^4 - a \\ &= a\, \left(r^4 - 1\right)\\ &= a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) \end{aligned}$ .

Therefore, the first equation becomes:

$a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right) = 150$ ..

Similarly, rewrite and simplify the second equation:

$\begin{aligned}&a\, r^3 - a\, r\\ &= a\, \left( r^3 - r\right) \\ &= a\, r\, \left(r^2 - 1\right) \end{aligned}$ .

Therefore, the second equation becomes:

$a\, r\, \left(r^2 - 1\right) = 48$ .

Take the quotient between these two equations:

$\begin{aligned}\frac{a\, \left(r^2 - 1\right) \, \left(r^2 + 1\right)}{a\cdot r\, \left(r^2 - 1\right)} = \frac{150}{48}\end{aligned}$ .

Simplify and solve for $r$ :

$\displaystyle \frac{r^2+ 1}{r} = \frac{25}{8}$ .

$8\, r^2 - 25\, r + 8 = 0$ .

Either $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ or $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ .

Assume that $\displaystyle r = \frac{25 - 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = -\frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= -\frac{1522\sqrt{41}}{41} \approx -238\end{aligned}$ .

Similarly, assume that $\displaystyle r = \frac{25 + 3\, \sqrt{41}}{16}$ . Substitute back to either of the two original equations to show that $\displaystyle a = \frac{497\, \sqrt{41}}{41} - 75$ .

Calculate the sum of the first five terms:

$\begin{aligned} &a + a\cdot r + a\cdot r^2 + a\cdot r^3 + a \cdot r^4\\ &= \frac{1522\sqrt{41}}{41} \approx 238\end{aligned}$ .

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2 years ago