N-78+_=37_N= WHAT IS N?

You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us

Elena-2011 [213]

Answer:

see the explanation

Step-by-step explanation:

we know that

step 1

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$r=10\%=10/100=0.10\\n=4$

substitute in the formula above

$A=P(1+\frac{0.10}{4})^{4t}$

$A=P(1.025)^{4t}$

Applying property of exponents

$A=P[(1.025)^{4}]^{t}$

$A=P(1.1038)^{t}$

step 2

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$r=10\%=10/100=0.10$

substitute in the formula above

$A=P(e)^{0.10t}$

Applying property of exponents

$A=P[(e)^{0.10}]^{t}$

$A=P(1.1052)^{t}$

step 3

Compare the final amount

$P(1.1052)^{t} > P(1.1038)^{t}$

therefore

Find the difference

$P(1.1052)^{t} - P(1.1038)^{t}$ ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

3 0

2 years ago

Using the provided measures determine the measure of angle K.

forsale [732]

Answer:

B. 34.90°

Step-by-step explanation:

✔️First, find GF using Trigonometric function:

Reference angle = 58°

Adjacent length = GF

Hypotenuse = 6 cm

Apply CAH, thus:

Cos 58 = Adj/Hyp

Cos 58 = GF/6

GF = 6*Cos 58

GF = 3.17951558 ≈ 3.18 cm

✔️Find angle K using the Sine Rule:

$\frac{sin(K)}{GF} = \frac{sin(G)}{KF}$

Substitute

$\frac{sin(K)}{3.18} = \frac{sin(64)}{5}$

Multiply both sides by 3.18

$sin(K) = \frac{sin(64)}{5}*3.18$

$sin(K) = 0.5716$

$K = sin^{-1}(0.5716)$

K = 34.8618741° ≈ 34.90°

5 0

2 years ago

6 cell phones weigh 46.2 ounces. Fourteen cell phones weigh 107.8 ounces. Does this represent a proportional relationship

Studentka2010 [4]

yes, because 46.2/6 = 7.7 ounces and 107.8/14 = 7.7 ounces

3 0

2 years ago

Read 2 more answers

MOREEEEEEEEEEEEEEEEEEE POINTSSSSSSSSSSSSSSSSSSSSSS

WINSTONCH [101]

Answer:

Thank you so much

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

The diameter of a circle has length 12. The center is at*(-5, 2). Give the equation

labwork [276]

Answer:

Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

Step-by-step explanation:

Let us consider the image attached in the answer area.

The center O has the co-ordinates i.e. (-5,2) and the diameter given is 12 units.

We know that radius is half of diameter.

$\text{Radius = }\dfrac{\text{Diameter}}{2}$

$\text{Radius = }\dfrac{12}{2}\\\Rightarrow \text{Radius = 6units}$

The equation for circle given the center and radius, can be represented as:

$(x-a)^{2}+ (y-b)^{2} = r^{2}$

Where (a,b) is the co-ordinate of center and r is the radius.

Let us consider the following formula:

$(p+q)^2 = p^{2}+ q^{2} +2pq\\(p-q)^2 = p^{2}+ q^{2} -2pq$

$(x-(-5))^{2}+ (y-2)^{2} = 6^{2}\\\Rightarrow (x+5)^{2}+ (y-2)^{2} = 36\\\Rightarrow x^{2} + 25 + 10x +y^{2} + 4-4y=36\\\Rightarrow x^{2} + 10x +y^{2} -4y-7=0$

Hence, Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

4 0

2 years ago