Questions: Computing the average daily balance, interest, and balance for a credit..
(a) Use the credit card statement to help fill in the table below. Note that there are 31 days in January. Also, a purchase increases the unpaid balance, a payment decreases the unpaid balance.
Date Transaction Transaction amount Unpaid balance Number of days at that balance Unpaid × Number balance of days
January 1 Beginning balance 1700.09 1700.09 3 days (from January 1 through January 3) balance er days
January 4 Payment 340.00 1360.09 days (from January 4 through January 12)
January 13 Purchase 61.95 ] 11 days (from January 13 through January 23)
January 24 Payment 800.00 8 days (from January 24 through January 31)
Total: 31 days
Total:
(b) Find the average daily balance. Write your answer to the nearest cent.
(c) Suppose the credit card company charges an interest rate of 1.7% on the average daily balance for January found in part (b). How much interest will be charged? Write your answer to the nearest cent.
(d) What will Manuel's beginning balance be for the month of February (including the interest for January found in part (c))?
Transcript text: Computing the average daily balance, interest, and balance for a credit..
(a) Use the credit card statement to help fill in the table below. Note that there are 31 days in January. Also, a purchase increases the unpaid balance, a payment decreases the unpaid balance.
\begin{tabular}{|c|c|c|c|c|c|}
\hline Date & Transaction & Transaction amount & Unpaid balance & Number of days at that balance & Unpaid $\times$ Number balance ${ }^{\times}$of days \\
\hline January 1 & Beginning balance & \$1700.09 & \$1700.09 & 3 days (from January 1 through January 3) & balance ${ }^{\text {er days }}$ \\
\hline January 4 & Payment & \$340.00 & \$1360.09 & $\square$ days (from January 4 through January 12) & $5 \square$ \\
\hline January 13 & Purchase & \$61.95 & \$] & 11 days (from January 13 through January 23) & $5 \square$ \\
\hline January 24 & Payment & \$800.00 & $5 \square$ & 8 days (from January 24 through January 31) & $5 \square$ \\
\hline
\end{tabular}
Total: 31 days
Total: $\$$
(b) Find the average daily balance. Write your answer to the nearest cent.
$\square$
(c) Suppose the credit card company charges an interest rate of $1.7 \%$ on the average daily balance for January found in part (b). How much interest will be charged? Write your answer to the nearest cent.
$\square$
(d) What will Manuel's beginning balance be for the month of February (including the interest for January found in part (c))?
$\square$
Solution
Solution Steps
Step 1: Calculate the unpaid balance and the product of unpaid balance and number of days for January 4th.
On January 4th, a payment of $340.00 was made. The unpaid balance becomes $1700.09 - $340.00 = $1360.09$.
From January 4th to January 12th, there are $12 - 4 + 1 = 9$ days.
The product of unpaid balance and number of days is $1360.09 \times 9 = 12240.81$.
Step 2: Calculate the unpaid balance and the product of unpaid balance and number of days for January 13th.
On January 13th, a purchase of $61.95 was made. The unpaid balance becomes $1360.09 + $61.95 = $1422.04$.
From January 13th to January 23rd, there are $23 - 13 + 1 = 11$ days.
The product of unpaid balance and number of days is $1422.04 \times 11 = 15642.44$.
Step 3: Calculate the unpaid balance and the product of unpaid balance and number of days for January 24th.
On January 24th, a payment of $800.00 was made. The unpaid balance becomes $1422.04 - $800.00 = $622.04$.
From January 24th to January 31st, there are $31 - 24 + 1 = 8$ days.
The product of unpaid balance and number of days is $622.04 \times 8 = 4976.32$.
Step 4: Calculate the sum of the products of unpaid balance and number of days.
The sum is $1700.09 \times 3 + 1360.09 \times 9 + 1422.04 \times 11 + 622.04 \times 8 = 5100.27 + 12240.81 + 15642.44 + 4976.32 = 37959.84$.
Step 5: Calculate the average daily balance.
The average daily balance is the sum of the products of unpaid balance and number of days divided by the total number of days, which is 31.
Average daily balance $= \frac{37959.84}{31} \approx 1224.51$.
Step 6: Calculate the interest charged.
The interest rate is $1.7\% = 0.017$.
Interest $= 1224.51 \times 0.017 \approx 20.82$.
Step 7: Calculate the beginning balance for February.
The beginning balance for February is the unpaid balance on January 31st plus the interest charged for January.
Beginning balance for February $= 622.04 + 20.82 = 642.86$.