1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kolbaska11 [484]
2 years ago
14

3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d

escribed below. a. The account pays 3% annual interest compounded monthly. b. The account pays 4% annual interest compounded continuously.​
Mathematics
1 answer:
pychu [463]2 years ago
8 0

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}

Where <em>A</em> is the final amount, <em>P</em> is the initial amount, <em>r</em> is the interest rate, <em>n</em> is the number of times compounded per year, and <em>t</em> is the number of years.

To obtain $4000 after two years, let <em>A</em> = 4000 and<em> t</em> = 2.

Because the account pays 3% interest compounded monthly, <em>r</em> = 0.03 and <em>n</em> = 12.

Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

\displaystyle A = Pe^{rt}

Where <em>e</em> is Euler's number.

Hence, let <em>A</em> = 4000, <em>r</em> = 0.04 and <em>t</em> = 2. Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}

In conclusion, about $3692.47 should be deposited.

You might be interested in
Please help I cant fail this math test thank you I appreciate it
Marta_Voda [28]

Answer:

d

Step-by-step explanation:

<33

4 0
3 years ago
Answer??????????????????????
ch4aika [34]
Here is the answer you are looking for: (7,13/3)

Please vote my answer brainliest. thanks!
5 0
2 years ago
What is the outlier of the data set 7, 15, 15, 15, 13, 7, 9, 11, 24
eduard

Answer:

24

Step-by-step explanation:

The outlier is the value that is far from the other values in the set

24 is far from the other values

7 0
3 years ago
If you know the answer tell me please and if you do you would be the best
Butoxors [25]
11 ⅓ gallons.

Explanation:

Since she sold 3⅓ gallons more on Sunday than she did on Saturday, you need to add 10⅔+3⅓. ⅓+⅔=3/3, or 1. 10+3=13, and 13+1=14. She sold 14 gallons on Sunday.

On Monday, she sold 2⅔ less than she did on Sunday, so we need to do 14-2⅔. 14-2 is 12, and 12-⅔= 11⅓. This means that she sold 11⅓ gallons on Monday.

Hope this helps :)
5 0
3 years ago
What is the place value for 5 in 35.052
snow_tiger [21]
The place value is the hundreths 
4 0
3 years ago
Read 2 more answers
Other questions:
  • To obtain the graph of y = (x - 8)2, shift the graph of y = x2 units.
    15·2 answers
  • Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink
    10·2 answers
  • What is the number that represents C in 4c + 16 = 35?
    10·2 answers
  • draw a rectangle and another figure that is not a rectangle by tracing lines on a grid paper.describe how to find the perimeter
    15·1 answer
  • Ng the Zero Product Property<br> Warm-Up<br> Which are solutions of the equation (x + 5)(x-3) = 0?
    11·1 answer
  • Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}. Identify the pairs of sets in which one is a subset of th
    9·2 answers
  • Can someone explain how to do this please?
    14·1 answer
  • When negative five is subtracted from a number the result is 10. Find the number.
    9·2 answers
  • Ms. Klein wants to put a fence around her garden. The garden is in the shape of a semi-circle with a radius of 12 feet. How much
    8·1 answer
  • Simplify 12x6 y7 18 x3y5.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!