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?

Answer 1

Gareth should make 18 ATM withdrawals every year for better deal.

Explanation:

Consider the provided information.

Gareth has $2,000 to invest and local bank will earn him 2.2% annual interest.

The amount earned by local bank is:
`\$2000* (2.2)/(100)=\$44`

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.

The amount earned by online account
`\$2000* (4.85)/(100)=\$97`

Savings account has no ATM withdrawal charges but online savings account charge $3.00 per withdrawal.

Let x is the number of times he withdrawal money.

`97-3x=44\\3x=53\\x=17.67\approx 18`

Hence, Gareth should make 18 ATM withdrawals every year for better deal.

Answer 2

Gareth has $2,000 to invest. Putting the money in a savings account at his local bank will earn him 2.2% annual interest.

Interest earned in local bank = 2000 * 22.2% = 2000 * 0.022 = 44

Putting the money in an online savings account will earn him 4.85% annual interest

Interest earned in online account = 2000 * 4.85% = 2000 * 0.0485 = 97

He will be charged $3 every time he makes an ATM withdrawal.

In online account, the interest is 97 . If he withdraws 18 times then

Total ATM fee is 18 * 3= 54 . so 97 - 54 = 43

43 is lower than 44 that is interest of local account.

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