Math  /  Numbers & Operations

QuestionLevel 2 Taylorl has the following summary statement over the period of 30 days for her credit. If her APR is 22.8%22.8 \%, her average daily balance is $1,840.25\$ 1,840.25. What is her new balance? \begin{tabular}{|l|l|l|l|l|l|l|l|} \hline & \begin{tabular}{l} Previous \\ Balance \end{tabular} & \begin{tabular}{l} Payments \\ Credits \end{tabular} & \begin{tabular}{l} New \\ Purchoses \end{tabular} & \begin{tabular}{l} Lote \\ Charge \end{tabular} & \begin{tabular}{l} Finance \\ Charge \end{tabular} & \begin{tabular}{l} New \\ Bolance \end{tabular} & \begin{tabular}{l} Minimum \\ Poyment \end{tabular} \\ \hline 1932.10 & 320.00 & 524.70 & 00 & & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? Given Taylorl's credit card statement with a previous balance, payments, new purchases, and a late charge, along with her average daily balance and APR, we need to calculate her new balance and finance charge. Watch out! Don't forget to convert the APR to a daily rate before calculating the finance charge!
Also, remember to add *everything* up correctly to get the new balance.

STEP 2

1. Calculate the Finance Charge
2. Calculate the New Balance

STEP 3

We're given an **APR (Annual Percentage Rate)** of 22.8%22.8\%.
To calculate the daily periodic rate, we'll divide the APR by **365**, the number of days in a year.
This tells us how much interest accrues each day. Daily Rate=APR365=22.8%365=0.2283650.0006246575\text{Daily Rate} = \frac{\text{APR}}{365} = \frac{22.8\%}{365} = \frac{0.228}{365} \approx 0.0006246575

STEP 4

Now, we'll multiply the **average daily balance** $1,840.25\$1,840.25 by the **daily periodic rate** to find the daily finance charge.
This tells us how much interest accrues each day on the average balance. Daily Finance Charge=Average Daily BalanceDaily Rate=$1,840.250.0006246575$1.15\text{Daily Finance Charge} = \text{Average Daily Balance} \cdot \text{Daily Rate} = \$1,840.25 \cdot 0.0006246575 \approx \$1.15

STEP 5

Finally, to get the total finance charge for the 30-day period, we multiply the daily finance charge by **30**. Finance Charge=Daily Finance Charge30=$1.1530$34.50\text{Finance Charge} = \text{Daily Finance Charge} \cdot 30 = \$1.15 \cdot 30 \approx \$34.50

STEP 6

Taylorl's **previous balance** was $1932.10\$1932.10.
This is our starting point.

STEP 7

She made **payments and credits** totaling $320.00\$320.00.
We subtract this from the previous balance: $1932.10$320.00=$1612.10\$1932.10 - \$320.00 = \$1612.10

STEP 8

Taylorl made **new purchases** worth $524.70\$524.70.
We add this to our running total: $1612.10+$524.70=$2136.80\$1612.10 + \$524.70 = \$2136.80

STEP 9

We calculated the **finance charge** to be $34.50\$34.50.
Let's add that in: $2136.80+$34.50=$2171.30\$2136.80 + \$34.50 = \$2171.30

STEP 10

There's no late charge this time, so we can skip this!
Lucky Taylorl!

STEP 11

Taylorl's new balance is $2171.30\$2171.30, and her finance charge is $34.50\$34.50.

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