Jackie makes an $800 deposit into a bank account earning 4.5% interest.
a. If the interest is compounded quarterly how much money will Jackie have in 10 years?
b. If the interest is compounded continuously how much money will Jackie have in 10 years?
C. If Jackie's money is compounded continuously, how long will it take her money to double?
d. If Jackie's money is compounded monthly, how long will it take her money to triple?

For part a, Jackie will have approximately $1217.62 after 10 years with quarterly compounding interest. For part b, Jackie will have approximately $1226.96 after 10 years with continuous compounding interest. For part c, it will take approximately 15.43 years for Jackie's money to double with continuous compounding interest. For part d, it will take approximately 38.51 years for Jackie's money to triple with monthly compounding interest.

For part a, to calculate the amount of money Jackie will have in 10 years with quarterly compounding interest, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years. Plugging in the values, we have A = 800(1 + 0.045/4)^(4*10), which gives us A ≈ $1217.62.

For part b, to calculate the amount of money Jackie will have in 10 years with continuous compounding interest, we can use the formula: A = P * e^(rt), where e is Euler's number and approximately equal to 2.71828. Plugging in the values, we have A = 800 * e^(0.045 * 10), which gives us A ≈ $1226.96.

For part c, to find out how long it will take Jackie's money to double with continuous compounding interest, we can use the formula: t = ln(2) / r, where t is the time in years and r is the interest rate. Plugging in the values, we have t = ln(2) / 0.045, which gives us t ≈ 15.43 years.

For part d, to find out how long it will take Jackie's money to triple with monthly compounding interest, we can use the formula: t = ln(3) / (n * ln(1 + r/n)), where t is the time in years, n is the number of times compounded per year, and r is the interest rate. Plugging in the values, we have t = ln(3) / (12 * ln(1 + 0.045/12)), which gives us t ≈ 38.51 years.

a. If the interest is compounded quarterly, Jackie will have approximately $1,313.63 in 10 years.

b. If the interest is compounded continuously, Jackie will have approximately $1,256.39 in 10 years.

c. If Jackie's money is compounded continuously, it will take approximately 15.4 years for her money to double.

d. If Jackie's money is compounded monthly, it will take approximately 62.47 years for her money to triple.

Step 1

To solve this problem, we can use the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Where:

- A is the amount of money accumulated after t years, including interest.

- P is the principal amount (the initial deposit).

- r is the annual interest rate (as a decimal).

- n is the number of times interest is compounded per year.

- t is the time the money is invested for, in years.

Given:

- [tex]\( P = \$800 \)[/tex]

-[tex]\( r = 0.045 \)[/tex] (4.5% as a decimal)

- n is either 4 for quarterly compounding or tends to infinity for continuous compounding.

Step 2

We'll calculate each part step by step:

a. Quarterly compounding:

- [tex]\( n = 4 \)[/tex]

- [tex]\( t = 10 \)[/tex]

Substituting into the formula:

[tex]\[ A = 800 \left(1 + \frac{0.045}{4}\right)^{4 \times 10} \]\[ A = 800 \left(1 + \frac{0.045}{4}\right)^{40} \]\[ A = 800 \left(1 + 0.01125\right)^{40} \]\[ A = 800 \times 1.01125^{40} \]\[ A = 800 \times 1.642032881 \]\[ A = \$1,313.63 \][/tex]

Step 3

b. Continuous compounding:

For continuous compounding, we use the formula:

[tex]\[ A = P e^{rt} \][/tex]

Where e is the base of the natural logarithm, approximately equal to 2.71828.

Substituting the values:

[tex]\[ A = 800 \times e^{0.045 \times 10} \]\[ A = 800 \times e^{0.45} \]\[ A = 800 \times 1.570482165 \]\[ A = \$1,256.39 \][/tex]

Step 4

c. To find out how long it takes for the money to double with continuous compounding, we use the formula:

[tex]\[ A = P e^{rt} \][/tex]

We need to solve for t  when [tex]\( A = 2P \):[/tex]

[tex]\[ 2P = P e^{0.045t} \]\[ 2 = e^{0.045t} \]\[ \ln(2) = 0.045t \]\[ t = \frac{\ln(2)}{0.045} \][/tex]

Substituting the values:

[tex]\[ t = \frac{\ln(2)}{0.045} \]\[ t = \frac{0.693}{0.045} \]\[ t = 15.4 \text{ years} \][/tex]

So, it takes approximately 15.4 years for Jackie's money to double with continuous compounding.

Step 5

d. To find out how long it takes for the money to triple with monthly compounding, we use the compound interest formula again, but this time we set [tex]\( A = 3P \)[/tex]:

[tex]\[ 3P = P \left(1 + \frac{0.045}{12}\right)^{12t} \]\[ 3 = \left(1 + \frac{0.045}{12}\right)^{12t} \]\[ \ln(3) = 12t \ln\left(1 + \frac{0.045}{12}\right) \]\[ t = \frac{\ln(3)}{12 \ln\left(1 + \frac{0.045}{12}\right)} \][/tex]

Substituting the values:

[tex]\[ t = \frac{\ln(3)}{12 \ln\left(1 + \frac{0.045}{12}\right)} \]\[ t = \frac{1.099}{12 \times 0.0037} \]\[ t = 62.47 \text{ years} \][/tex]

So, it takes approximately 62.47 years for Jackie's money to triple with monthly compounding.

Explain what is pi and how many number it has

A punch bowl has a capacity of
8 quarts. How many cups can the
punch bowl hold?
A 16 cups
B 24 cups
C 32 cups
D 48 cups​

What is the value of the expression 6x (2.2+12.8)-4

Quinn mailed four postcards that each cost $0.25, five letters that each cost $0.44, two large envelopes that each cost $0.80, and one small package for $5.10. Which cost on the list of mailing fees on Quinn’s receipt would skew the mean?

the cost of a postcard
the cost of a letter
the cost of a large envelope
the cost of the small package

The sum of three numbers is -39.22. One of the numbers is 22.8. The other two numbers are equal to each other. What is the value of the other two numbers?

(07.01)Amanda created a table to help her represent the sample space of spinning a spinner and flipping a coin
Result of spin
Result of coin tossRed Green
Yellow Blue
Heads
Red, heads Green, heads Yellow, heads Blue, heads
Tails
Red, tails Green, tails Yellow, tails Blue tails
What is the probability that the result of the spin is blue and the coin lands heads up?
2
8
3
8
1
8
4
8

Solve the equation.
5u - 10 = 70

John was given a math equation. He completed it in 5 seconds. Is his answer correct? If it is, show how he got the answer. Show your work. See picture down below.

Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation.

Which scatter plot would have a trend line with a negative y-intercept?

what is the area of the square units

Rewrite the equation by completing the square.
x² + 4x = 0​

the probabiltiy for snow today is 0.6 the probabiltiy foe anow tomorrrw of 0.4. the pr ability for snow both days is 0.1. fins the probability that it will snow at least one if the two days

please help me solve this quadratic equation ​

Help me please again :))

can someone help me really please​

Select three expressions that are equivalent to 2x(4x+8y) Please include explanation.
Will choose brainliest

If there are 6 hours in a school day, 5 school days in a week, 4 school weeks in
a month and 9 months in a school year, how many hours are there in a school
year?

hours in a school year​

which box plot represents a data set with a lower quartile or 24 and an upper quartile of 42

Maria spent 19 days traveling in South America how many hours did she spent traveling in South America

Which statements are true about the locations of points A and B? Select all that apply.
1 Point A is at (0, –2).
2 Point A is at (0, –4).
3 Point A is at (–4, 0).
4 Point B is at (–4, –3).
5 Point B is at (–8, –6).
6 Point B is at (–8, –7).

Which graph best represents the cost to mail a package based on weight categories?
Plz help

Which of the following numbers can be expressed as a decimal that terminates? 3/2, 2/3, 3/4, 5/7

The figure below has one base
and eight lateral faces. Find its surface
area to the nearest whole number.

4. If a student is chosen at random from
those who participated in the survey,
what is the probability that the student
participates in school sports, given that
the student is a male?
Answer choices:
0.379
0.476
0.524
0.621

What is the slope of the line through (-1, 4) and (1, -2)?

How many 4-digit numbers are multiples of at least one of these two numbers: 2; 5.
How many 4-digit numbers are multiples of both 2 and 5?
How many 4-digit numbers are neither multiples of 2 nor multiples of 5?

Kendrick brought a 5 kilogram can of peanuts for $8.75. What is the unit price?

Consider the equation, 3x+4y=12.
Write the equation in slope-intercept form.
Identify the y-intercept.

Identify the slope.

A jar contains 11 brown and 18 blue marbles. A marble is drawn at random. What is the probability that the marble is not blue?

A. 18⁄29

B. 1⁄11

C. 11⁄18

D. 1⁄18

E.11⁄29