John finances his daughter's college education by making deposits into a fund earning interest at an annual effective rate of 8%. For 18 years he deposits X at the beginning of each month. In the 16th through the 19th years, he makes a withdrawal of 25,000 at the beginning of each year. The final withdrawal reduces the fund balance to zero. Calculate X.

Answers

Answer 1

Answer:

Monthly payment = 241.925

Step-by-step explanation:

Effective interest rate is the actual interest paid at the end of the year AFTER compounding.  Most credit cards charge x% ("APR", annual percentage rate)annually.  Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.

Here, effective (annual) interest rate is 8%.  We need the monthly rate, i.

(1+i)^12 = 1.08

Solving, we have i = 0.6434% monthly approximately

To balance the deposits and withdrawals, we note that the last withdrawal is the beginning of year 19, and the last deposit is the last month of year 18.  We therefore conclude that the "future values" fall on the same day, and that they are equal.

We consider the annual deposits D (accumulated at the end of the year, and annual withdrawals W are in separate accounts.  By the end of the operations, one will balance the other (they are equal).

We will need the following formula to calculate future value F given the periodic amount, A, interest rate per period, i, and the number of periods.

F(A,i,n) = A*((1+i)^n-1)/i

Step 1:

calculate the future value of the withdrawals

A = W = 25000 (annual withdrawal)

i = 8% (effective annual interest)

n = 4 years (beginning of 16,17,18,and 19th years)

F(A,i,n) = A*((1+i)^n-1)/i

= 25000( (1+0.08)^4 - 1)/(0.08)

= 112652.80

This is also the total deposit after eighteen years.

Step 2:

calculate the future value of the annual deposits D

A = D (total of annual deposits)

i = 8% (effective annual interest)

n = 18 years

Future value of deposits

F(A,i,n) = A*((1+i)^n-1)/i

= D( (1+0.08)^18 -1 ) / 0.08

= 37.45024373981167D

Since this must equal the total withdrawal, we equate the two to calculate D.

37.45024373981167D=112652.80

and solve for D

D = 112652.80 / 37.45024373981167

= $3008.0659

Step 3

Calculate monthly deposit, X

Effective interest rate is the actual interest paid at the end of the year AFTER compounding.  Most credit cards charge x% ("APR", annual percentage rate)annually.  Since it is compounded monthly, each month the balance increases by (x//12)%, and by the end of the year, you will be paying effectively (x//12)^12 %, which is the effective interest rate.

Here, effective (annual) interest rate is 8%.  We need the monthly rate, i.

(1+i)^12 = 1.08

The actual monthly interest rate is therefore

i = 1.08^(1/12)-1

Over a 12 month period, (one year), the monthly amount X to accumulate an annual amount D (=$3008.0659) is therefore given by

D = X*((1+i)^n-1)/i

3008.0659 = X*(1.08-1)/(1.08^(1/12)-1)

or the monthly amount

X = $3008.0659 / ( 1.08^(1/12)-1)

= 241.925 per month.

=


Related Questions

Working together, Sam and Charlie can change all the light bulbs in the office building in 3 hours. It would have taken Charlie 8 hours to do the job alone.

A table showing Rate in part per hour, Time in hours, and Part of Light Bulbs Changed. The first row shows,Sam, and has r, 3, and r times 3. The second row shows Charlie, and has StartFraction 1 Over 8 EndFraction, 3 and StartFraction 1 Over 8 EndFraction times 3.
Which equation can be used to solve for the rate, r, for Sam to change all the light bulbs in the office building by himself?

3r = 3 r equals StartFraction 3 Over 8 EndFraction.
3r + 3 r plus StartFraction 3 Over 8 EndFraction equals 1. = 1
r + StartFraction 1 Over 3 EndFraction r plus StartFraction 3 Over 8 EndFraction r equals 1.r = 1
r + StartFraction 1 Over 3 EndFraction r plus StartFraction 1 Over 8 EndFraction r equals 1.r = 1

Answers

Answer:

B

3r + 3/8=1

Step-by-step explanation:

EDGE

Answer:

b

Step-by-step explanation:

determinants and inverses

Answers

Answer:

qustion number 1 the last one .

qustion number 2 the first one .

pls help me find num 6 & 7

Answers

Number 6 is B. And Number 7 is C

Answer: The answer of number 6 is D. The answer of number 7 is D.

Step-by-step explanation:

For number 6, y=110° because they are vertical angles. x=y=70°=180°-110°

For number 7, 180°-63°=117°=a

Twenty planes are at an airport. Eight planes take off, then five planes land, then 7
more take off, then 9 land. How many planes are left at the airport? PLS HELPP

Answers

Answer:

19

Step-by-step explanation:

20 - 8 = 12

12 + 5 = 17

17 - 7 = 10

10 + 9 = 19

Write the equation of the line in slope-intercept form

Answers

Equation in slope intercept form: y= -1/2x + 3

The volume of the following figure is
240 in² which of the following is the missing side length?
A. 7 in
B. 6 in
C. 8 in
D. 5 in

Answers

Answer:

B cause it same

Step-by-step explanation:

If am wrong correct me thanks

Which term BEST describes the following statement?

You are looking at a map of the United States, and it is assumed that you already know which direction is north.
A. Proof
B. Theorem
C. Common Notion
D. Conjecture

Answers

The answer would be B.) Theorem :)

Answer:

B. THEORM - this would be your answer

Step-by-step explanation:

Hope this helps :)

The volume of a right rectangular prism can be found by finding the product 3(6)(12) Which expression could also be used to determine the volume of this prism? 36(6) 2(3 + 12 + 6) 4(3)(12) 12 + 6 +3​

Answers

Answer:

D

Step-by-step explanation:

Another fairly simple one, pretty much a free Brainliest and 30 points.

Answers

Answer:

Solution given:

[tex]8\frac{7}{12}-3\frac{1}{3}=\frac{8*12+7}{12}-\frac{3*3+1}{3}[/tex]

=[tex]\frac{103}{12}-\frac{10}{3}[/tex]

taking lcm

=[tex] \frac{103-10*4}{12}=\frac{63}{12}=\frac{21}{4}=5\frac{1}{4}[/tex]

Answer:

5 1/4

Step-by-step explanation:

8 7/12 - 3 1/3

We need to get a common denominator of 12

8 7/12 - 3 1/3 *4/4

8 7/12 - 3 4/12

5 3/12

Simplifying the fraction

5 1/4

There were 60 7th grade students last year in CHAMPS. This year, there are 48 7th grade students. What is the percent decrease from last year to this year?

Answers

20%

Hope this helps! :)

______________

PLEASE PLEASE HELP ME PLEASE PLEASSE

EXPLANATION = BRAINLIEST

ANSWER NEEDS TO BE IN SIMPLEST FORM

please help

Answers

Answer:

the answer will be r=48-3 your answer will be 45

Answer:

(6/5) π in^2 or 1.2 π in^2

Step-by-step explanation:

the area of a circle and the area of one circle sector are proportional.

Area of the circle = radius^2 * π = 3^2 π = 9π in^2

the hidden date is that the centre angle of a circumference is 360 degrees

we have now to use a proportion that has this meaning:

if the area is 9π in^2 when the angle is 360 degrees, what is the area when the angle is 48 degrees?

9π : 360 = x : 48

x = (48 *9π)/360 = (6/5) π in^2

Question 10 (4 points) Point A, located at (4, 1), is reflected over the x-axis and then translated (x - 3, y + 7). Write the location of A' ​

Answers

Answer:

(1, 6)

Step-by-step explanation:

Reflecting (4, 1) over the x-axis makes it (4, -1), the translation (x - 3, y + 7) means moving (4, -1) 3 left and 7 up

Pamela wants to learn more about the career preferences of students in her school. She interviews a number of students from the advanced science class. Why is this sample likely to be biased?

Answers

It is an advanced science class, therefore the students will most likely have a preference in science related careers, over representing science, and under representing anything else.

Answer:

I hope this helps

Step-by-step explanation:

7. Find the volume of space consumed by the toilet paper without the center cylinder.
4cm
SHOW YOUR WORK!
*
14cm
12 cm
I
Volume

Answers

Answer:

7. 1583.36 cm³

8. 13,627.18 m³

Step-by-step explanation:

Volume of space consumed by the paper = volume of outer cylinder - volume of center cylinder

✔️Volume of Outer Cylinder:

Volume = πr²h

r = ½(12) = 6 cm

h = 14 cm

Volume = π*6²*14

Volume = 1583.36 cm³

✔️Volume of center cylinder:

Volume = πr²h

r = ½(4) = 2 cm

h = 14 cm

Volume = π*2²*14

Volume = 175.93 cm³

✅Volume of space of the toilet paper = 1583.36 - 175.93 = 1583.36 cm³

8. Volume of the solid = volume of the cone + volume of the cylinder

✔️Volume of the cone = ⅓πr²h:

r = 13 m

h = 14 m

V = ⅓*π*13²*14

V = 2,477.67 m³

✔️Volume of the cylinder = πr²h

r = 13 m

h = 21 m

V = π*13²*21

V = 11,149.51 m³

✅Volume of the solid = 2,477.67 + 11,149.51 = 13,627.18 m³

After how many seconds ,t, will the object be 75 meters above the ground

Answers

Answer:

It will be above the ground in C

Step-by-step explanation:

plz help I need to finish this Geometry
How do you know what method (SSS, SAS, ASA, AAS) to use when proving triangle congruence?

Answers

It depends on what type of triangle you’re dealing with, and what is marked similar.

what is 8690 rounded off to the neareset hundred?
am just asking​

Answers

Answer:

8700

Step-by-step explanation:

If it is 8,690 and you round to the nearest hundred it would add one to 90 making it 8,700

Answer:

Did not necessarily round up or down, but to the hundred that is nearest to 8690.

8690 rounded to the nearest hundred is: 8700

Help PLEASE!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

=22 m²

Step-by-step explanation:

Total area= Area of rectangle 1 + Area of rectangle 2

Tres hermanas deciden comenzar una cadena, donando cada una a tres personas $5.000 en un mismo día; con la condición que a quienes ellas ayuden también deberán hacer lo mismo con tres personas al día siguiente. ¿Al cabo de una semana cuántas personas han participado en la cadena? ¿Finalizado el quinto día cuánto dinero se ha donado?

Answers

Answer:

Al cabo de una semana, 2187 personas han participado en la cadena, y al cabo del quinto día se habrán donado $1215000.

Step-by-step explanation:

Dado que tres hermanas deciden comenzar una cadena, donando cada una a tres personas $5.000 en un mismo día; con la condición que a quienes ellas ayuden también deberán hacer lo mismo con tres personas al día siguiente, para determinar, al cabo de una semana, cuántas personas han participado en la cadena, y finalizado el quinto día cuánto dinero se ha donado, se deben realizar los siguientes cálculos:

3^7 = X

2,187 = X

(3^5) x 5000 = X

243 x 5000 = X

1,215,000 = X

Por lo tanto, al cabo de una semana, 2187 personas han participado en la cadena, y al cabo del quinto día se habrán donado $1215000.

find the slope! i have more to come so please help:(

Answers

Answer:  -3/2

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

Work Shown:

Rise = -3

Run = 2

Slope = rise/run = -3/2 = -1.5

----------------

Notes:

The rise and run correspond to the vertical and horizontal portions of the triangle shownThe rise is negative because we're going downhill when moving from left to right, so that also means the slope is negative. The run is always positive.

Answer:

m = - 3 / 2

Rise : -3

Run : 2

Step-by-step explanation:

According to the picture,

first coordinate : ( 2 , 1 )

second coordinate : ( 4 , - 2 )

Formulae : m=(y2-y1)/(x2-x1)

Substituting,

m = ( - 2 - 1 ) / ( 4 - 2 )

m = - 3 / 2

If this helps you, please mark brainliest!

Pls only help if you know the correct answer! Thanks! :)

Answers

answer:
b
step-by-step explanation:
a and c aren’t negative so we can get rid of those answers
d is backwards
b is the only correct answer

Answer:

Line B.

Step-by-step explanation:

Line A and line C don't have a negative side, so we can assume that those are wrong. On line D, -2 1/4 is supposed to be closer to -2, not -4 and -3.6 is supposed to be closer to -4, not -2, so line B is the correct answer.

Graph the solution of 3x - 5<-8 or 2x – 7 >3.

Answers

Answer:

To be Honest I Really Don't know What are the Answers?

A) 3x -7 = 2x+5

3x-2x= 5+7

1x= 12

Resposta final: x=12 e so fazer sequindo o exemplo

Determine the value of angle V in the picture below. Please help

Answers

Answer:

40 degrees

Step-by-step explanation:

Mathematically, the sum of two opposite interior angles of a triangle equals the exterior angle

Thus, we have it that;

60 + (7x + 5) = 20x

60 + 5 = 20x-7x

13x = 65

x = 65/13

x = 5

But angle V = 7x + 5

V = 7(5) + 5

V = 35 + 5

V = 40

Please please help me if you can I really need it
If you can please answer all of the questions
They should be simple if you know basic geometry
Thank you so much

Answers

Answer:

1- c:25

2-cant help

3- A:2,8

4-cant help


On this necklace the ratio of black beads to white beads is 1:3
How many more black beads do you need to add to make the
ratio of black to white 3:1?​

Answers

Answer:

8 more black beads.

Step-by-step explanation:

B=1

W=3

B:W = 1: 3

Make

B:W = 3:1 = 9:3

So we need (9-1) = 8 more black beads.

Answer: chupa verga maricon de mierda

Step-by-step explanation:

Find the surface area of a sphere
Show all the work

Answers

Answer:

452cm2

Step-by-step explanation:

surface area of sphere =4πr2

so 4π62 which equals to 452.39.

hope this helps u understand:)

65 70 75 80 85
Brand A
HIH
15
50
60
70
85
Brand B
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Price ($)
Which statement is the most appropriate comparison of the spreads?
O A. The interquartile range (IQR) for brand A, $20, is less than the IQR
for brand B. $70.
O B. The median for brand A, $75, is greater than the median for brand
B, $60.
O C. The interquartile range (IQR) for brand A, $10, is less than the IQR
brand B. $20.
O D. The interquartile ranges (IQRs) for brands A and B are both $20.

Answers

Given:

Two box plots for Brand A and Brand B.

To find:

The correct statement for the given box plots.

Solution:

In a box plot, the left end of the box represents the first quartile [tex](Q_1)[/tex], right end of the box represents the third quartile [tex]Q_3[/tex] and the line inside the box represents the median.

The interquartile range of a data set is:

[tex]IQR=Q_3-Q_1[/tex]

From the box plot of Brand A, it is clear that

[tex]Q_1=70[/tex]

[tex]Median=75[/tex]

[tex]Q_3=80[/tex]

So, the interquartile range (IQR) for brand A is:

[tex]IQR=80-70[/tex]

[tex]IQR=10[/tex]

From the box plot of Brand B, it is clear that

[tex]Q_1=50[/tex]

[tex]Median=60[/tex]

[tex]Q_3=70[/tex]

So, the interquartile range (IQR) for brand B is:

[tex]IQR=70-50[/tex]

[tex]IQR=20[/tex]

The median for brand A, $75, is greater than the median for brand B, $60.

The interquartile range (IQR) for brand A, $10, is less than the IQR

brand B. $20.

Therefore, the correct options are B and C.

- Andrew gave half of his money to support a local charity. From what was left, he spent
$22.75 on a present for his sister. If he had $183.89 left over, how much did he have to
begin with?

Answers

Okay so basically you need to see what half of the amount he started with was to do that you need to add both of the numbers ^^^ = 206.64. Which is half of the starting number so you times by two. =$413.28

Help me find B in these 4 equations please

Answers

11) b= 25°

12) b= 63°

13) b= 93°

14) b= 46°

My little sister need help!

Answers

tell your little sister she can borrow ur calculator
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