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

Answer 1

Answer:

Option c. 18 withdrawals is correct

Step-by-step explanation:

Gareth has to invest = $2,000

His local bank gives 2.2% annual interest and gives him the ability to make ATM withdrawals without any charges.

In an online savings gives 4.85% annual interest, but charges $3 every time he makes an ATM withdrawal.

Let us find the amount of interest earned from the local bank.

The amount of interest earned from Local Bank = 2.2% of 2000

= $\frac{22}{100}$ × 2000

= 0.022 × 2000 = $44

The amount of interest earned from online savings = 4.85% of 2000

= $\frac{4.85}{100}$ × 2000

= 0.0485 × 2000 = $97

As it is given that savings account has no ATM withdrawal charges but online savings account charge $3.00 per withdrawal.

so we  need to make x withdrawals from both accounts such that:

97 - 3x = 44

Let us solve for x.

Upon subtracting 97 from both sides of or equation we will get,

97 - 97 - 3x = 44 - 97

3x = -53

$\frac{3x}{-3}=\frac{-53}{-3}$

x = 17.666 rounded to 18

Therefore, Gareth must make 18 ATM withdrawals every year for the local savings account to be a better deal than the online savings account.