you have $5,400 to deposit. if you deposit the money in a savings account at your local bank, you will earn…

you have $5,400 to deposit. if you deposit the money in a savings account at your local bank, you will earn 1.49% annual interest and will be able to make atm withdrawals at your banks atms. if you deposit the money in an online savings account, you will earn 4.44% annual interest, but you will be charged $5 every time you make an atm withdrawal. assuming that your atm withdrawals do not reduce the amount of interest you earn, roughly how many times a year can you make an atm withdrawal in order for the local savings account to be a better deal than the online savings account? a. 32 b. 27 c. 22 d. 15

you have $5,400 to deposit. if you deposit the money in a savings account at your local bank, you will earn 1.49% annual interest and will be able to make atm withdrawals at your banks atms. if you deposit the money in an online savings account, you will earn 4.44% annual interest, but you will be charged $5 every time you make an atm withdrawal. assuming that your atm withdrawals do not reduce the amount of interest you earn, roughly how many times a year can you make an atm withdrawal in order for the local savings account to be a better deal than the online savings account? a. 32 b. 27 c. 22 d. 15

Answer

Answer:

c. 22

Explanation:

Step1: Calculate local bank interest

Interest from local bank = $5400\times0.0149 = 80.46$

Step2: Calculate online bank interest

Interest from online bank = $5400\times0.0444= 239.76$

Step3: Set up inequality

Let $n$ be the number of ATM - withdrawals. We want $80.46>239.76 - 5n$.

Step4: Solve inequality for $n$

First, move the terms: $5n>239.76 - 80.46$. Then $5n>159.3$. So $n>\frac{159.3}{5}=31.86$. But we want the local bank to be better, so we consider the largest integer value of $n$ for which the local - bank is still better. If $n = 22$, the cost of withdrawals from the online bank makes the local bank a better deal.