Answer: B) Option 1, $510.00
Explanation:
Step 1
We will determine the amount earned using option 1
Initial amount deposited into the account is $500 This means that the principal is P, so
P = 500
It was compounded annually. This means that it was compounded once in a year. So
n = 1
The rate at which the principal was compounded is 2%. So
r = 2/100 = 0.02
It was compounded for just a year. So
n = 1
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.02/1)^1×1
A = 500(1.02) = $510
Step 2
We will determine the amount earned using option 2
Initial amount deposited into the account is $500 This means that the principal is P, so
P = 500
It was compounded monthly. This means that it was compounded 12 times in a year. So
n = 12
The rate at which the principal was compounded is 2%. So
r = 2/100 = 0.02
It was compounded for just a year. So
n = 1
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.02/12)^12×1
A = 500(1.0017)^12 = 510.29
Approximately $510
Since option 2 has an annual fee of $1, the amount earned will be
510 - 1 = $509
She should choose option 1
She will have $510 in option 1