gareth has $2,000 to invest. putting the money in a savings account at his local bank will earn him 2.2%…

gareth has $2,000 to invest. putting the money in a savings account at his local bank will earn him 2.2% annual interest and gives him the ability to make atm withdrawals from that banks 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 gareths 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? a. 8 b. 14 c. 18 d. 25

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 banks 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 gareths 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? a. 8 b. 14 c. 18 d. 25

Answer

Explanation:

Step1: Calculate local bank interest

The interest from the local bank is calculated using the simple - interest formula $I = Prt$. Here, $P=$2000$, $r = 0.022$ (since $2.2%=0.022$) and $t = 1$ year. So, $I_{local}=2000\times0.022\times1 = 44$.

Step2: Calculate online bank interest

The interest from the online bank is $I_{online}=2000\times0.0485\times1=97$.

Step3: Set up an inequality

Let $n$ be the number of ATM withdrawals. The net interest from the online bank after $n$ withdrawals is $I_{net - online}=97 - 3n$. We want to find $n$ such that $I_{local}>I_{net - online}$, that is $44>97 - 3n$.

Step4: Solve the inequality

First, add $3n$ to both sides: $3n + 44>97$. Then subtract 44 from both sides: $3n>97 - 44$, so $3n>53$. Divide both sides by 3: $n>\frac{53}{3}\approx17.67$.

Answer:

c. 18