Question 1197305
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An APR of 18% means the monthly interest rate is (18%)/12 = 1.5%
The decimal form of 1.5% is 0.015
We move the decimal point two spots to the left.


Here's what the table would look like for The Silver Card.
<table border = "1" cellpadding = "5"><tr><td>Day</td><td>Balance ($)</td><td>Interest Charged ($)</td><td>Notes</td></tr><tr><td>Oct 1st</td><td>0</td><td></td><td></td></tr><tr><td>Oct 25th</td><td>1800</td><td></td><td>Purchased the $1800 computer</td></tr><tr><td>Nov 1st</td><td>1800</td><td>0</td><td>Interest = 1.5% of $0 balance on Oct 1st</td></tr><tr><td>Nov 10th</td><td>1200</td><td></td><td>Payment of $600 (so 1800-600 = 1200)</td></tr><tr><td>Dec 1st</td><td>1227</td><td>27</td><td>Interest = 1.5% of 1800 (not 1200)</td></tr><tr><td>Dec 10th</td><td>627</td><td></td><td>Payment of $600 (so 1227-600 = 627)</td></tr><tr><td>Jan 1st</td><td>645.41</td><td>18.41</td><td>Interest = 1.5% of 1227 (not 627)</td></tr><tr><td>Jan 10th</td><td>0</td><td></td><td>Payment of $645.41 (on Jan 10th) to fully pay off balance</td></tr></table>


The table highlights key dates in Oct, Nov, Dec, and Jan. 
Oct 1st is of course when the balance is $0.
Oct 25th is when the computer was purchased, which bumps the balance up to $1800.


Nov 1st is when the first interest charge is calculated. But since the starting balance of the previous month (Oct 1st) was $0, this means we dont have to worry about interest here. 
More technically
interest charged = 1.5% of $0 = 0.015*0 = 0
Therefore, the balance stays at $1800 on Nov 1st.


On Nov 10th, the $600 payment is fully processed.
That brings the balance down to 1800-600 = 1200 dollars.


On Dec 1st, we take 1.5% of the balance on Nov 1st to calculate the interest for this month.
interest = 1.5% of 1800 = 0.015*1800 = 27 dollars
Be sure to NOT use the 1200.
The $27 interest charge bumps the balance up to 1200+27 = 1227 dollars.


On Dec 10th, a payment of $600 brings the balance down to 1227-600 = 627


On Jan 1st, the interest is calculated.
1.5% of balance on Dec 1st = 1.5% of $1227 = 0.015*1227 = 18.405 which rounds to 18.41
This brings the balance up to 627+18.41 = 645.41 dollars.


On Jan 10th is when the final payment is made, because the goal is to pay off the entire balance by this point.
The payment here is $645.41


Total amount paid back = (payment on Nov 10th)+(payment on Dec 10th)+(payment on Jan 10th)
Total amount paid back = (600)+(600)+(645.41)
Total amount paid back = 1845.41


Subtract off the principal, aka amount loaned, to find the total interest
1845.41 - 1800 = 45.41


Or you could add up the values in the interest column
0+27+18.41 = 45.41


The total amount of interest for The Silver Card is $45.41


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Now onto The Gold Card.


ADB = Average Daily Balance


The chart is going to be a bit larger compared to the previous one.
Below the table is an explanation how the ADB values are calculated and the interest charged.
<table border = "1" cellpadding = "5"><tr><td>Timespan</td><td>Number of days</td><td>Balance ($)</td><td>ADB ($)</td><td>Interest ($)</td><td>Notes</td></tr><tr><td>Oct 1st to Oct 24th</td><td>24</td><td>0</td><td></td><td></td><td></td></tr><tr><td>Oct 25th to Oct 31st </td><td>7</td><td>1800</td><td></td><td></td><td>Purchase of $1800 (on Oct 25th)</td></tr><tr><td></td><td></td><td></td><td>406.45</td><td></td><td>End of Billing Cycle</td></tr><tr><td>Nov 1st to Nov 9th</td><td>9</td><td>1806.21</td><td></td><td>6.21</td><td></td></tr><tr><td>Nov 10th to Nov 30th</td><td>21</td><td>1206.21</td><td></td><td></td><td>Payment of $600 (on Nov 10th)</td></tr><tr><td></td><td></td><td></td><td>1386.21</td><td></td><td>End of Billing Cycle</td></tr><tr><td>Dec 1st to Dec 9th</td><td>9</td><td>1226.72</td><td></td><td>20.51</td><td></td></tr><tr><td>Dec 10th to Dec 31st</td><td>22</td><td>626.72</td><td></td><td></td><td>Payment of $600 (on Dec 10th)</td></tr><tr><td></td><td></td><td></td><td>800.91</td><td></td><td>End of Billing Cycle</td></tr><tr><td>Jan 1st to Jan 9th</td><td>9</td><td>638.96</td><td></td><td>12.24</td><td></td></tr><tr><td>Jan 10th to Jan 31st</td><td>22</td><td>0</td><td></td><td></td><td>Payment of $638.96 (Jan 10th) to fully pay off balance</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>End of Billing Cycle</td></tr></table>


Review this article to refresh your memory on how to calculate the ADB
<a href = "https://www.thebalancemoney.com/average-daily-balance-finance-charge-calculation-960236">https://www.thebalancemoney.com/average-daily-balance-finance-charge-calculation-960236</a>


Here's the ADB side calculation for the month of October.
ADB = ( (24 days)*($0) + (7 days)*($1800) )/(31 days)
ADB = $406.45


The interest is found by this formula
interest = (APR*ADB*n)/365
where,
APR = annual percentage rate = annual interest rate of the card
ADB = Average Daily Balance
n = number of days in the billing cycle


We have
APR = 0.18
ADB = 406.45
n = 31 days in oct


Let's calculate the interest for October
interest = (APR*ADB*n)/365
interest = (0.18*406.45*31)/365
interest = 6.21367397260273
interest = 6.21


The ADB and interest calculations for November and December will follow the same ideas.
Use n = 30 for November and n = 31 for December.


Add up all the values in the "interest" column
6.21+20.51+12.24 = 38.96
This is the total interest charged on the Gold Card.



Now let's compare the total interest for each card.
Silver = $45.41
Gold = $38.96
We see the gold is better and the difference is 45.41-38.96 = 6.45 dollars

 

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Answers: 
Gold Card interest charged: <font color=red>$38.96</font>
Silver Card interest charged: <font color=red>$45.41</font>


Which card is better and by how much? <font color=red>The Gold Card</font> is better by <font color=red>$6.45</font>
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