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

With an annual interest rate of 2.2%, interest would be I=prt. P=2000. r=0.022. t=1. That would give you a product of $2044 annually because $44 in interest has been made. Meanwhile as for the online savings account, P=$2000 but r=0.0485, which then gives you a new value of I=97. $97 interest has been made so $2097. That is $53 additional interest earned as opposed to the savings account. Assuming $3 was to be deducted with every transaction, you want to put it in this format:3x=53. That would equal 17.66~. Again since we can't have a decimal in our answer, we round up to 18. That means we'll need to make at least 18 withdrawals($54) to make a profit as opposed to the savings account.

Answer 2

What a strange question. How could withdrawals fail to change the interest earned?! Anyway... How much does $2000 earn in a year at 2.2%? How much does $2000 earn in a year at 4.85%? What the difference in interest credits? How many $3 ATM transactions does it take to eat that up?