Answer:
a. Ameribank-$15,157.50
b. Capital Two-$4,646.25
Step-by-step explanation:
a. Tad's savings is $15,000, we calculate his total amount at the end of the year for each bank:
#Ameribank
[tex]A=P+I=P+PRT\\\\=15000+15000\times 0.0105\times 1\\\\=\$15,157.50[/tex]
#Huffington( we use the effective rate to calculate the compound amount):
[tex]i_m=(1+i/m)^m-1\\\\=(1+0.0095/12)^[12}-1=0.009541\\\\A=P(1+i_m)^n\\\\=15000(1.009541)^1\\\\=\$15,143.12[/tex]
#Sixth-Third, Take 1 yrs=52 weeks:
[tex]i_m=(1+i/m)^m-1\\\\=(1+0.01/52)^{52}-1=0.01005\\\\A=15000(1.01005)^1\\\\=\$15,150.74[/tex]
#Hence, Ameribank is the best option as his money grows to $15,157.50 which is greater than all the remaining two options.
b. We use the compound interest formula [tex]A=P(1+r/n)^{nt}[/tex] to determine which bank gives the best option:
#Capital Two. r=3.75%, n=12,t=4
[tex]A=P(1+r/n)^{nt}\\\\=4000(1+0.0375/12)^{12\times4}\\\\=\$4,646.25[/tex]
#J.C Morgan, t=2, r=3.55% n=12
[tex]A=P(1+r/n)^{nt}\\\\=4000(1+0.0355/12)^{12\times 2}\\\\=\$4,293.87[/tex]
#Silverman Slacks, n=12,t=3, r=3.65%
[tex]A=P(1+r/n)^{nt}\\\\=4000(1+0.0365/12)^{12\times3}\\\\=\$4,462.14[/tex]
We compare the investment amounts after t years:
[tex]Capital>Silver>Morgan=4646.25>4462.14>4293.87[/tex]
Hence, Capital two is the best option with an investment amount of $4,646.25
