Question

Need help ASAP 20 POINTS!

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