PLEASE HELP!!!! URGENT !!!!! (40 points!!!)

For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the

Stella [2.4K]

Answer:

(a) The future value after 9 years is $7142.49.

(b) The effective rate is $r_E=4.759 \:{\%}$ .

(c) The time to reach $13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of $P$ dollars is invested at a rate of interest $r$ compounded continuously for $t$ years, the compound amount is

$A=Pe^{rt}$

(a) From the information given

$P=4700$

$r=4.65\%=\frac{4.65}{100} =0.0465$

$t=9 \:years$

Applying the above formula we get that

$A=4700e^{0.0465\cdot 9}\\A=7142.49$

The future value after 9 years is $7142.49.

(b) The effective rate is given by

$r_E=e^r-1$

Therefore,

$r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}$

(c) To find the time to reach $13,000, we must solve the equation

$13000=4700e^{0.0465\cdot t}$

$4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88$

3 0

3 years ago

Miguel earns extra money working two weekends with his dad. He is saving to buy a new bike that costs $140. Heather says that Mi

Eddi Din [679]

it doesn't divide equally

5 0

4 years ago

The ingredients are doubled in the large Totally Turkey Sandwich. On Wednesday, three times as many customers ordered the regula

11111nata11111 [884]

Answer:

45 slices of turkey used

Step-by-step explanation:

In order to figure out this problem we first need to calculate the total amount of sandwiches that were ordered. Since 27 regular sandwiches were ordered and we know that three times as many customers ordered the regular sandwich as the large sandwich. Then we simply divide 27 by 3 to find out how many large sandwiches were ordered.

27 / 3 = 9 large sandwiches.

Now, assuming that each regular sandwich only takes one slice of turkey, we can multiply 9 by 2 since each large sandwich takes double the slices and add that to 27 to calculate the total number of slices used in all of the sandwiches for that day.

(9*2) + 27 = s

18 + 27 = s

45 = s

There were a total of 45 slices of turkey used.

8 0

4 years ago

Match the information on the left with the appropriate equation on the right.

solmaris [256]

Answer:

Step-by-step explanation:

1). Equation of a line which has slope 'm' and y-intercept as 'b' is,

y = mx + b

If slope 'm' = 1 and y-intercept 'b' = -3

Equation of the line will be,

y = x - 3

x - y = 3

2). Equation of a line having slope 'm' and passing through a point (x', y') is,

y - y' = m(x - x')

If the slope 'm' = 1 and point is (-1, 2),

The the equation of the line will be,

y - 2 = 1(x + 1)

y = x + 1 + 2

y = x + 3

x - y = -3

3). Equation of a line passing through two points $(x_1, y_1)$ and $(x_2,y_2)$ will be,

$y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$

If this line passes through (-2, 3) and (-3, 4),

$y-3=\frac{(4-3)}{(-3+2)}(x+2)$

y - 3 = -1(x + 2)

y = -x - 2 + 3

y = -x + 1

x + y = 1

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B20%7D%7B16%7D%20%2A%20100" id="TexFormula1" title=" \frac{20}{16} * 100" alt=" \f

mart [117]

125% because sixteen is equal to a whole which is equal to one-hundered and one fourth of sixteen is four and sixteen plus four is twenty. one fourth of one-hundered is twenty-five so you add the twenty-five to the one-hundered and you get 125%

8 0

3 years ago