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3 years ago

7

After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth

1 answer:

Irina-Kira [14]3 years ago

5 0

9514 1404 393

Answer:

19 years

Step-by-step explanation:

The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...

A = P(1 +r/n)^(nt)

Solving for t, we get ...

t = log(A/P)/(n·log(1 +r/n))

Using the given values, we find t to be ...

t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000

The investment will be worth $213,022 after 19 years.

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klasskru [66]

Answer:

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=0,\:x=6$

Step-by-step explanation:

Considering the system of the equations

$\begin{bmatrix}2x-7y=12\\ -x+15y=-6\end{bmatrix}$

$\mathrm{Isolate}\:x\:\mathrm{for}\:2x-7y=12$

$2x-7y+7y=12+7y$

$2x=12+7y$

Divide both sides by 2

$\frac{2x}{2}=\frac{12}{2}+\frac{7y}{2}$

$x=\frac{12+7y}{2}$

$\mathrm{Subsititute\:}x=\frac{12+7y}{2}$

$\begin{bmatrix}-\frac{12+7y}{2}+15y=-6\end{bmatrix}$

$-\frac{12+7y}{2}+15y=-6$

$\mathrm{Multiply\:both\:sides\:by\:}2$

$-\frac{12+7y}{2}\cdot \:2+15y\cdot \:2=-6\cdot \:2$

$-\left(12+7y\right)+30y=-12$

$-12+23y=-12$

$-12+23y+12=-12+12$

$23y=0$

$\mathrm{Divide\:both\:sides\:by\:}23$

$\frac{23y}{23}=\frac{0}{23}$

$y=0$

$\mathrm{For\:}x=\frac{12+7y}{2}$

$\mathrm{Subsititute\:}y=0$

$x=\frac{12+7\cdot \:0}{2}$

$x=\frac{12}{2}$

$x=6$

$\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}$

$y=0,\:x=6$

4 0

4 years ago

X/3 in a fraction -4=5

Elena-2011 [213]

X/3 - 4 = 5
x/3 = 9
x=27

7 0

3 years ago

Mauricio scored a total of 34.42 points in five gymnastic

Olegator [25]

Answer:

Mauricio's score for each event is 7.

Step-by-step explanation:

Mauricio scored a total of 34.42 points in five gymnastic events.

We can round off his score as 35.

To find Mauricio's score for each event, divide total score and no of events as follows :

$n=\dfrac{35}{5}\\\\=7$

Hence, Mauricio's score for each event is 7.

3 0

3 years ago

The scale on a map of Virginia shows that 1 inch represents 20 miles the actual distance from Richmond Virginia to Washington DC

DedPeter [7]

Answer:

5.5 inches

Step-by-step explanation:

Proportions:

1 inch ⇔ 20 miles

W inch ⇔ 110 miles

W = 110*1/20

W = 5,5 inch

7 0

3 years ago

Diamonds have a density of 3.5 LaTeX: \frac{g}{cm^3}g c m 3. How big is a diamond that has a mass of 0.10 g?

liubo4ka [24]

For this case we have that by definition, the density is given by:

$d = \frac {M} {V}$

Where:

M: It is the mass of the diamond

V: It is the volume of the diamond

According to the data of the statement we have:

$d = 3.5 \frac {g} {cm ^ 3}\\M = 0.10 \ g$

So the volume is:

$V = \frac {M} {d}\\V = \frac {0.10 \ g} {3.5 \frac {g} {cm ^ 3}}\\V = 0.02857\\V = 0.03 \ cm^3$

Thus, the volume of the diamond is approximately $0.03 \ cm ^ 3$

Answer:

$0.03 \ cm ^ 3$

3 0

3 years ago