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 must withdraw a total of 17 times in one year to make the local savings account more worth it than online. In the online account, Gareth makes 94 per year, if he withdraws 17 times, he gets a total fee of 51 (17 x 3). 94-51 is 43 which is lower than the interest of the local account (44).

Answer 2

18 ATM withdrawals.

Explanation:

Let x be the number of ATM withdrawals.

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

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

`\text{The amount of interest earned from local bank}=2,000* (2.2)/(100)`

`\text{The amount of interest earned from local bank}=2,000* 0.022`

`\text{The amount of interest earned from local bank}=44`

We are also told that putting the money in an online savings account will earn him 4.85% annual interest.

`\text{The amount of interest earned from online savings account bank}=2,000* (4.85)/(100)`

`\text{The amount of interest earned from online savings account bank}=2,000* 0.0485`

`\text{The amount of interest earned from online savings account bank}=97`

We are told that local bank charges nothing for ATM withdrawals, while online savings account charges $3 per ATM 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`

`(-3x)/(-3)=(-53)/(-3)`

`x=17.6666666\approx 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.