(a) use the credit - card statement to help fill in the table below. note that there are 30 days in june…

(a) use the credit - card statement to help fill in the table below. note that there are 30 days in june. also, a purchase increases the unpaid balance, and a payment decreases the unpaid balance.\ndate\ttransaction\ttransaction amount\tunpaid balance\njune 1\tbeginning balance\t \t$2600.04\njune 8\tpayment\t$850.00\t$1750.04\njune 21\tpurchase\t$79.35\t$1829.39\njune 25\tpayment\t$500.00\t$1329.39\nunpaid balance × number of days\n$1829.39×7 days (from june 1 through june 7)\n$1750.04×13 days (from june 8 through june 20)\n$1829.39×4 days (from june 21 through june 24)\n$1329.39×6 days (from june 25 through june 30)\ntotal: 30 days\ntotal: $56244.7\n(b) find the average daily balance. write your answer to the nearest cent.\n(c) suppose the credit - card company charges an interest rate of 1.5% on the average daily balance for june found in part (b). how much interest will be charged? write your answer to the nearest cent.\n(d) what will lisas beginning balance be for the month of july (including the interest for june found in part (c))?

(a) use the credit - card statement to help fill in the table below. note that there are 30 days in june. also, a purchase increases the unpaid balance, and a payment decreases the unpaid balance.\ndate\ttransaction\ttransaction amount\tunpaid balance\njune 1\tbeginning balance\t \t$2600.04\njune 8\tpayment\t$850.00\t$1750.04\njune 21\tpurchase\t$79.35\t$1829.39\njune 25\tpayment\t$500.00\t$1329.39\nunpaid balance × number of days\n$1829.39×7 days (from june 1 through june 7)\n$1750.04×13 days (from june 8 through june 20)\n$1829.39×4 days (from june 21 through june 24)\n$1329.39×6 days (from june 25 through june 30)\ntotal: 30 days\ntotal: $56244.7\n(b) find the average daily balance. write your answer to the nearest cent.\n(c) suppose the credit - card company charges an interest rate of 1.5% on the average daily balance for june found in part (b). how much interest will be charged? write your answer to the nearest cent.\n(d) what will lisas beginning balance be for the month of july (including the interest for june found in part (c))?

Answer

Explanation:

Step1: Calculate average daily balance

The average - daily - balance formula is $\text{Average Daily Balance}=\frac{\sum_{i = 1}^{n}(\text{Unpaid balance}_i\times\text{Number of days}_i)}{\text{Total number of days}}$. We have: [ \begin{align*} &\text{Sum}=18200.28 + 22750.52+7317.56 + 7976.34+5624.47\ &=56249.17 \end{align*} ] The total number of days in June is 30. So, $\text{Average Daily Balance}=\frac{56249.17}{30}\approx1874.97$.

Step2: Calculate interest

The interest rate is $1.5%$ on the average daily balance. The interest formula is $I = r\times B$, where $r$ is the interest rate and $B$ is the balance. $r=0.015$ and $B = 1874.97$. So, $I=0.015\times1874.97 = 28.12455\approx28.12$.

Step3: Calculate July beginning balance

The beginning balance for July is the unpaid balance on June 30 plus the interest. The unpaid balance on June 30 is the last unpaid balance in the table, which is $5624.47$. So, the beginning balance for July is $5624.47+28.12 = 5652.59$.

Answer:

(b) $$1874.97$ (c) $$28.12$ (d) $$5652.59$