you have $6,500 to deposit. if you deposit the money in a savings account at your local bank, you will earn…

you have $6,500 to deposit. if you deposit the money in a savings account at your local bank, you will earn 1.45% 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 2.25% interest, but you will be charged $4 every time you make an atm withdrawal. assuming that your atm withdrawals do not reduce the amount of interest you earn, how many atm withdrawals must you make in a year for the local savings account to be a better deal than the online savings account?\na. 5\nb. 12\nc. 14\nd. 10

you have $6,500 to deposit. if you deposit the money in a savings account at your local bank, you will earn 1.45% 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 2.25% interest, but you will be charged $4 every time you make an atm withdrawal. assuming that your atm withdrawals do not reduce the amount of interest you earn, how many atm withdrawals must you make in a year for the local savings account to be a better deal than the online savings account?\na. 5\nb. 12\nc. 14\nd. 10

Answer

Explanation:

Step1: Calculate local bank interest

The interest earned in the local bank is calculated using the simple - interest formula $I = Prt$. Here, $P=$6500$, $r = 0.0145$ (since $1.45%=0.0145$) and $t = 1$ year. So, $I_{local}=6500\times0.0145=$94.25$.

Step2: Calculate online bank interest and charges

The interest earned in the online bank is $I_{online - interest}=6500\times0.0225=$146.25$ (since $2.25% = 0.0225$). Let the number of ATM withdrawals be $n$. The total cost of ATM withdrawals is $C = 4n$. The net interest in the online bank is $I_{online}=146.25-4n$.

Step3: Set up the inequality

We want to find when the local bank is a better deal, so we set up the inequality $I_{local}>I_{online}$. Substituting the values of $I_{local}$ and $I_{online}$, we get $94.25>146.25 - 4n$.

Step4: Solve the inequality for $n$

First, add $4n$ to both sides: $94.25 + 4n>146.25$. Then subtract $94.25$ from both sides: $4n>146.25 - 94.25$, so $4n>52$. Divide both sides by $4$: $n > 13$.

Answer:

C. 14