Question

gareth has $2,000 to invest. putting the money in a savings account at his local bank will earn him 2.2% annua 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, roughl how many atm withdrawals must gareth make every year for the local savings account to be a better deal tha the online savings account?
a. 8
b. 14
c. 18
d. 25

please select the best answer from the choices provided

a
b
c

Explanation:

Step1: Calculate interest for local bank

Local bank interest rate: \(2.2\% = 0.022\), principal \(P = 2000\).
Interest from local: \(I_{local}=2000\times0.022 = 44\) dollars.

Step2: Calculate interest for online bank

Online bank interest rate: \(4.85\% = 0.0485\).
Interest from online: \(I_{online}=2000\times0.0485 = 97\) dollars.

Step3: Find interest difference

Difference in interest: \(97 - 44 = 53\) dollars.

Step4: Relate to ATM fees

Let \(n\) be number of withdrawals. Fee per withdrawal: \$3.
We need \(3n > 53\) (so online’s net gain < local’s gain).
Solve \(n > \frac{53}{3}\approx17.67\). So \(n\approx18\) (since 17 withdrawals would make \(3\times17 = 51 < 53\), 18 makes \(3\times18 = 54 > 53\)).

Answer:

c. 18