Question

Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest and gives him the ability to make ATM withdrawals from that bank’s ATMs. Putting the money in an online savings account will earn him 4.85% annual interest, but he will be charged $3 every time he makes an ATM withdrawal. Assuming that Gareth’s ATM withdrawals do not affect the amount of interest he earns, roughly how many ATM withdrawals must Gareth make every year for the local savings account to be a better deal than the online savings account? a. 8 b. 14 c. 18 d. 25 Please select the best answer from the choices provided A B C D

Answer 1

Answer:

• Option C. 18

Explanation:

1. Local savings account

• Investment: $2,000
• Annual interest: 2.2% × $2,000 = 0.022 × $2,000 = $44
• Total value: $2,000 + $44 = $2,044.

2. Online savings account

• Investment: $2,000
• Annual interest: 4.85% × $2,000 = 0.0485 × $2,000 = $97
• Charges for ATM withdrawal: 3x
• Total value: $2,000 + $97 - 3x = $2,097 - 3x

3. How many ATM withdrawals must Gareth make every year for the local savings account to be a better deal than the online savings account?

Solve the inequality:

• 2,044 > 2,097 - 3x
• 3x > 2,097 - 2,044
• 3x > 53
• x > 53/3
• x > 17.67

Thus, Gareth has to make 18 ATM withdrawals in a year for the local savings account to be a better deal than the online savings account.