Question

Need help ASAP 20 POINTS!
Compare Accounts A and B. Then complete the sentences.
There are two rectangles. The first rectangle with heading Account A and content principal: $16,000; annual interest: 3%, compound quarterly number of years: 10 and the second rectangle with heading Account B and content principal: $16,000; annual interest: 3%, compound monthly number of years: 10.

Account __________
is worth the most after 10 years. It will have a value of $
________________ .

Answer 1

Answer:

Account B

Value=$21,589.66

Step-by-step explanation:

#We determine the compounded amount after 10 years for each account using the formula:

$A=P(1+i_m)^n, i_m=(1+i/m)^m-1, m-compoundings \ per \ year$

#For account A:

Given principal is $16,000, i=3% and n=10, m=4:

$(1+i_m)=(1+i/m)^m\\\\=(1+0.03/4)^4=1.03034\\\\\therefore A=16000(1.03034)^{10}\\\\=21573.75$

#For account B:

Given principal is $16,000, i=3% and n=10, m=12:

$(1+i_m)=(1+i/m)^m\\\\=(1+0.03/12)^{12}=1.03042\\\\\therefore A=16000(1.03042)^{10}\\\\\\\\=21589.66$

We compare the amounts after 10 years and get the difference:

$B>A\\\\B-A=21589.66-21573\\\\=\ 15.91$

Hence, account B has the most value after 10 years and has a value of $21,589.66

Answer 2

The account that would be worth more in 10 years is Account B and it would have a value of  $21,589.66.

The formula that can be used to determine the value of the accounts after 10 years is:

FV = P (1 + r)^nm

• FV = Future value  
• P = Present value  
• R = interest rate  
• m = number of compounding
• N = number of years

Account A:

$16,000 x (1 + 3%/4)^(4 x 10)

$16,000 x (1.0075)^40 = $21,573.58

Account B:

$16,000 x (1 + 3%/12)^(12 x 10)

$16,000 x (1.0025)^120 = $21,589.66

To learn more about future value, please check: https://brainly.com/question/14640433