Question

Please help!

Option 1: Compounding annually with no fee.
Option 2: Compounding monthly with a $1 annual fee.


Emma puts $500 in the bank with a 2% annual interest rate. The bank has two options listed above. If Emma plans to not touch the money for one year, which plan should she choose? How much money will she have with that plan after one year?
A) Option 1, $509.00
B) Option 1, $510.00
C) Option 2, $509.09
D) Option 2, $510.09

Answer 1

Given the two options above, in order to come up with the best plan we have to calculate the future value of money in each plan.
compound interest is given by:
`FV=p(1+ (r)/(100))^n`

Option 1
p=$500
r=2%=0.02
t=1 year

`FV=500(1+0.02)^1=$510`

Option 2
p=$500
r=2/12=1/6
n=1*12=12
hence:

`FV=500(1+( (1)/(6))/(100))^(12)`
=$509.09
Comparing the two plans above, option 1 is the best.

b] Option 1 is the best because she will secure $510 as compared to option 2 which has interest rate that reduces her amount by $1 after one year due to annual charges. The total amount of money she will have at the end of the plan is $510.