Question

At River Bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge.
Calculate the income earned in one month on the checking account for a customer with an account balance of $1,000.

A.
$4.25

B.
$5.50

C.
$6.75

D.
$7.25

Checking account earnings at Baker’s Bank are expressed by the equation: I = -0.09x + 10.2.

While the earnings at Elite Bank are modeled by: I = -0.02x + 7.5.

In both cases, x is the number of checks written.

At what number of checks will Elite Bank start generating more checking account income than Baker's Bank?

A.
12

B.
25

C.
39

D.
42

Emilio’s checking account had a balance of 728.32 at the beginning of the week. He wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. He also deposited his paycheck in the amount of $1,109.90. What is his account balance at the end of the week?

A.
$1,192.35

B.
$1,222.86

C.
$1,540.52

D.
$1,614.96

Answer 1

Solution:

1. Account balance of customer=  $ 1,000

Interest earned in checking account= 0.75%

Financial charge= $ 2

So, income earned in one month on the checking account

= 0.75% of 1,000 - $ 2

$=\frac{0.75}{1,00\times 100}\times 1,000 -2\\\\=7.50-2\\\\=5.50$

Option (B) $ 5.50

2. Checking account earnings at Baker’s Bank  (I) = -0.09 x + 10.2

    The earnings at Elite Bank are modeled by: I = -0.02 x + 7.5

The number of checks when Elite Bank start generating more checking account income than Baker's Bank is given by inequality,

→→ -0.02 x +7.5 > -0.09 x +10.2

→→ -0.02 x + 0.09 x > 10.2 - 7.5

→→0.07 x > 2.7

→→$x>\frac{2.7}{0.07}\\\\ x>\frac{270}{7}\\\\ x>38 \frac{2}{7}$

So, the number of checks should be a whole number.

So, when number of checks = 39,→→Option (C) Elite Bank will start generating more checking account income than Baker's Bank.

3. Total amount in Emilio's checking account at the end of the week=( Beginning Balance= $ 728.32) -[4 Checks=( 99.48 +33.50 +18.23 +72.05)]+ $ 1109.90(Paycheck amount)

= 1109.90 + 728.32 - 223.26

= $1614.96 →→ Option (D)