MATHEMATICS MIDDLE SCHOOL

You want to have $3000 in your savings account after 3 years. Find the amount you should deposit for each of the situations described below.a. the account pays 3% annual interest compounded quarterly
b. the account pays 2.25% annual interest compounded monthly
c. the account pays 2% annual interest compounded daily
(SHOW YOUR WORK)

Answers

Answer 1
Answer: A) take the annual interest and divide it by 4 since it is compounded quarterly.
.03 ÷ 4 = .0075.  Add 1 to include your principal.  1.0075 and raise it to the 12th power since you will be doing this 4 times a year for 3 years (4 x 3 =12).
Since you want 3000 at the end of this period you should do:

3000 ÷ (1.0075¹²) and you get $2742.71  which is how much you should put in.

B) .001875 is the monthly rate of 2.25%  (.0225 divided by 12)
This time we have to do it to the 36th power since there are 36 months in 3 years.
Don't forget to add the 1 to include your money.
3000 ÷ (1.001875¹²) = $2804.36

C) 2% compounded daily means .02 ÷ 365 = (about) .00005479 
Once again we add our principal by putting a 1 in front 1.00005479  
3000 ÷ (1.00005479¹⁰⁹⁵) (1095 because 365 x 3 years = 1095 days)
= $2825.31

Just to emphasize why I always added 1.  Since I am dividing, dividing by 1 givesyou the same as you start with (3000 ÷1 is still 3000)  The small numbers after the 1 reduce the amount (3000) to the amount you will have to put in to realize $3000 at the end of each time period.
Answer 2
Answer:

Final answer:

To have $3000 in the savings account after 3 years, you should deposit $2688.97 for situation a, $2669.29 for situation b, and $2667.99 for situation c.

Explanation:

To find the amount you should deposit for each situation, we can use the formula for compound interest:

A = P(1 + (r/n))^(nt)

where A is the final amount, P is the principal amount (the initial deposit), r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.

Using the given information, we can calculate:

  1. For situation a (3% annual interest compounded quarterly), we have A = $3000, r = 3% = 0.03, n = 4 (since interest is compounded quarterly), and t = 3. Rearranging the formula, we get:
    P = A / (1 + (r/n))^(nt) = $3000 / (1 + (0.03/4))^(4*3) = $2688.97 (rounded to two decimal places).
  2. For situation b (2.25% annual interest compounded monthly), we have A = $3000, r = 2.25% = 0.0225, n = 12 (since interest is compounded monthly), and t = 3. Substituting these values into the formula, we get:
    P = A / (1 + (r/n))^(nt) = $3000 / (1 + (0.0225/12))^(12*3) = $2669.29 (rounded to two decimal places).
  3. For situation c (2% annual interest compounded daily), we have A = $3000, r = 2% = 0.02, n = 365 (since interest is compounded daily), and t = 3. Plugging these values into the formula, we get:
    P = A / (1 + (r/n))^(nt) = $3000 / (1 + (0.02/365))^(365*3) = $2667.99 (rounded to two decimal places).

Learn more about Compound interest here:

brainly.com/question/14295570

#SPJ2

Related Questions

Solve the equation: -5/4n  = 40My answer choices are: A: n = -50, B: n = -32, C: n = 32, D: n = 50
ther are 6 blades on each windmill how many total blades are on 7 windmills ? use a fives fact to solve
Can someone help me with these questions?
Winnie the Pooh goes to the honey store to buy a case of honey for the winter. The case of 24 jars of honey cost $27.60. What is the cost of each jar?A) $0.87 B) $1.00 C) $1.15 D) $62.40
What is 9.375 Rounded to the nearest hundredth

Al's Awesome Autos advertised a special sale on cars - Dealer cost plus 5%!! Jack and Margaret ought a luxury sedan for $23,727.90. What was the dealer's cost? (HINT: Using a propotion, think of the new price being 105% of the cost of the car)Why do you need to calculate 105% of the cost

Answers

105/23727.90=100/x
105x=23727.90x100
105x=2372790
(105x)/105=2372790/105
x=22598

dealers cost is $22,598

the 105% is the 100% price of the car plus the 5% of that tax or whatever it is

Imagine that this graph represents the distance Brianna travels to get to her babysitting job with respect to time. Describe a relation that the graph may represent.

Answers

Answer:Brianna left home and drove 3 miles in 6 minutes. She then stopped for 4 minutes to pick up coffee. Finally, she traveled the last 4 miles in 6 minutes to arrive at her babysitting job.

-1 1/3+-3/5? Please help

Thank you

Answers