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Math  /  Numbers & Operations

QuestionQuestion 1 (1 point) E. Yossi Hussein uses a credit card that carries an 18\% □\square APR and uses the adjusted balance method for calculating finance charges. Yossi's statement listed these facts: previous balance, \310.33;purchases,$219.67;fees,$75;payments,$150;andcredits,$62.69.Ifthecreditcardcompanyisesadailyperiodicrate,whatisYossi′sfinancechargeandnewbalanceona31daybillingcycle?a310.33; purchases, \$219.67; fees, \$75; payments, \$150; and credits, \$62.69. If the credit card company ises a daily periodic rate, what is Yossi's finance charge and new balance on a 31 day billing cycle? a \1.49;$293.80 1.49 ; \$ 293.80 b $2.98;$273.99\$ 2.98 ; \$ 273.99 c $1.49;$393.80\$ 1.49 ; \$ 393.80 d $3.60;$393.80\$ 3.60 ; \$ 393.80

Studdy Solution

STEP 1

What is this asking? We need to find out how much Yossi will be charged in finance fees and what his new balance will be after 31 days, using his credit card details. Watch out! Don't forget to calculate the **daily rate** from the annual rate and apply it to the **adjusted balance**!

STEP 2

1. Calculate the adjusted balance
2. Determine the daily periodic rate
3. Calculate the finance charge
4. Calculate the new balance

STEP 3

First, let's figure out Yossi's **adjusted balance**.
This is the balance after accounting for payments and credits.
We'll start with the **previous balance** and adjust it with **purchases**, **fees**, **payments**, and **credits**.
Adjusted Balance=Previous Balance+Purchases+Fees−Payments−Credits\text{Adjusted Balance} = \text{Previous Balance} + \text{Purchases} + \text{Fees} - \text{Payments} - \text{Credits}

STEP 4

Plug in the numbers:
Adjusted Balance=310.33+219.67+75−150−62.69\text{Adjusted Balance} = 310.33 + 219.67 + 75 - 150 - 62.69

STEP 5

Calculate it step by step:
310.33+219.67=530.00310.33 + 219.67 = 530.00530.00+75=605.00530.00 + 75 = 605.00605.00−150=455.00605.00 - 150 = 455.00455.00−62.69=392.31455.00 - 62.69 = 392.31So, the **adjusted balance** is $392.31\$392.31.

STEP 6

Next, we need to find the **daily periodic rate**.
The annual percentage rate (APR) is given as **18\%**.
To convert this to a daily rate, we divide by the number of days in a year (365).
Daily Periodic Rate=18%365\text{Daily Periodic Rate} = \frac{18\%}{365}

STEP 7

Convert the percentage to a decimal and calculate:
Daily Periodic Rate=0.18365≈0.00049315\text{Daily Periodic Rate} = \frac{0.18}{365} \approx 0.00049315

STEP 8

Now, let's calculate the **finance charge** using the adjusted balance and the daily periodic rate over the 31-day billing cycle.
Finance Charge=Adjusted Balance⋅Daily Periodic Rate⋅31\text{Finance Charge} = \text{Adjusted Balance} \cdot \text{Daily Periodic Rate} \cdot 31

STEP 9

Substitute the values:
Finance Charge=392.31⋅0.00049315⋅31\text{Finance Charge} = 392.31 \cdot 0.00049315 \cdot 31

STEP 10

Calculate it step by step:
392.31⋅0.00049315≈0.1935392.31 \cdot 0.00049315 \approx 0.19350.1935⋅31≈5.99850.1935 \cdot 31 \approx 5.9985Rounding to two decimal places, the **finance charge** is $6.00\$6.00.

STEP 11

Finally, let's find the **new balance** by adding the finance charge to the adjusted balance.
New Balance=Adjusted Balance+Finance Charge\text{New Balance} = \text{Adjusted Balance} + \text{Finance Charge}

STEP 12

Substitute the values:
New Balance=392.31+6.00\text{New Balance} = 392.31 + 6.00

STEP 13

Calculate:
New Balance=398.31\text{New Balance} = 398.31So, the **new balance** is $398.31\$398.31.

STEP 14

The finance charge is $6.00\$6.00 and the new balance is $398.31\$398.31.

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