I will make you Brianliest

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: B) Option 1, $510.00

Step-by-step 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