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Hatshy [7]
3 years ago
11

How long will it take to have R30 000 for a trip to Europe if I invest R20 000 now at 15% per year, compounded quarterly?

Mathematics
1 answer:
maw [93]3 years ago
3 0

<span>Compound  interest  formula</span>

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

 

Where

<span>
A= Future value
P = the Principal (the initial amount of money) 
r = annual interest rate</span>

t = time

<span>n= number of times compounded in one t






Remark
----------------------------------------------------------------------------------

r is generally a percentage like 3%, 7% etc and are applied in the formula as 0.03, 0.07..., 

the interest is compounded generally annually (n=1), quarterly (n=4), monthly (n=12), etc...

t is in years,


In our problem:

</span>

A= 30 000

P =20 000

r = 15%=0.15

time = t = ?

n= 4

applying the formula:

A=P(1+ \frac{r}{n} )^{nt}\\\\30,000=20,000(1+ \frac{0.15}{4} )^{4t}\\\\ \displaystyle{\frac{30,000}{20,000} =(1.0375)^{4t}

\displaystyle{ 1.5={(1.0375^4)}^t\\\\

1.5=1.159^t\\\\ \displaystyle { t=log_{1.159}1.5=2.75

75% of 12 months is 3/4 of 12 months, which is 9 months

Answer: 2 years, 9 months

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Step-by-step explanation:

there is 4 people and so you do 58 divided by 4=14.5 so there will be .5 left over

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Evaluate the expression when m=25 and n=2
lawyer [7]

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Step-by-step explanation:

4 0
3 years ago
A triangle with vertices at A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A′(0, 0), B′(0, 10), a
Vesnalui [34]

Answer:

2.5

Step-by-step explanation:

A triangle ABC with vertices A(0, 0), B(0, 4), and C(6, 0) is dilated to form a triangle A'B'C' with vertices A′(0, 0), B′(0, 10), and C′(15, 0). If the center of dilation is point A or A' (the origin), then

\dfrac{A'B'}{AB}=\dfrac{A'C'}{AC}.

Since

  • AB=4;
  • A'B'=10;
  • AC=6;
  • A'C'=15,

then the scale factor of the dilation is

k=\dfrac{10}{4}=\dfrac{15}{6}=2.5.

3 0
3 years ago
If f(x) = x^4-x^3+x^2 and g(x)= -x^2, where x does not = 0, what is (f/g)(x)?
Korvikt [17]

For this case we have the following functions:

f (x) = x ^ 4-x ^ 3 x ^ 2\\g (x) = - x ^ 2

By definition of composition of functions we have to:(f \ g) (x) = \frac {f (x)} {g (x)}

So:

\frac {f (x)} {g (x)} = \frac {x ^ 4-x ^ 3 x ^ 2} {- x ^ 2} = \frac {x ^ 4} {- x ^ 2} +\frac {-x ^ 3} {- x ^ 2}+ \frac {x ^ 2} {- x ^ 2} =

By definition of division of powers of the same base we have to place the same base and subtract the exponents:

\frac {f (x)} {g (x)} = - x ^ 2+x-1

ANswer:

(\frac {f} {g}) (x) = - x ^ 2 +x-1

3 0
3 years ago
Solve -2/3x &gt; 8 or -2/3x &lt; 4.
vekshin1
<h3>Answer: Choice C</h3>

{x | x < -12 or x > -6}

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

Explanation:

Let's solve the first inequality for x.

(-2/3)x > 8

-2x > 8*3

-2x > 24

x < 24/(-2)

x < -12

The inequality sign flips when we divide both sides by a negative value.

Let's do the same for the second inequality.

(-2/3)x < 4

-2x < 4*3

-2x < 12

x > 12/(-2)

x > -6

The conclusion of each section is that x < -12 or x > -6 which points us to <u>choice C</u> as the final answer.

Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.

8 0
2 years ago
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