SOLUTION: Hello, my problem is: On October 25, you plan to purchase a $1,800 computer by using one of your two credit cards. The Silver Card charges 18% interest and calculates interest base

Question 1197305: Hello, my problem is: On October 25, you plan to purchase a $1,800 computer by using one of your two credit cards. The Silver Card charges 18% interest and calculates interest based on the balance on the first day of the previous month. The Gold Card charges 18% interest and calculates interest based on the average daily balance. Both cards have a $0 balance as of October 1. The closing date is the end of the month for each card.
Your plan is to make a $600 payment in November, make a $600 payment in December, and pay off the remaining balance in January. All your payments will be received and posted on the 10th of each month. No other charges will be made on the account. (Round your answers to the nearest cent.)
(a)
Based on this information, calculate the interest (in $) charged by each card for this purchase.
Gold card:
Silver card:
Which card is the better deal and by how much (in $)?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

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.

Day	Balance ($)	Interest Charged ($)	Notes
Oct 1st	0
Oct 25th	1800		Purchased the $1800 computer
Nov 1st	1800	0	Interest = 1.5% of $0 balance on Oct 1st
Nov 10th	1200		Payment of $600 (so 1800-600 = 1200)
Dec 1st	1227	27	Interest = 1.5% of 1800 (not 1200)
Dec 10th	627		Payment of $600 (so 1227-600 = 627)
Jan 1st	645.41	18.41	Interest = 1.5% of 1227 (not 627)
Jan 10th	0		Payment of $645.41 (on Jan 10th) to fully pay off balance

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.

Timespan	Number of days	Balance ($)	ADB ($)	Interest ($)	Notes
Oct 1st to Oct 24th	24	0
Oct 25th to Oct 31st	7	1800			Purchase of $1800 (on Oct 25th)
			406.45		End of Billing Cycle
Nov 1st to Nov 9th	9	1806.21		6.21
Nov 10th to Nov 30th	21	1206.21			Payment of $600 (on Nov 10th)
			1386.21		End of Billing Cycle
Dec 1st to Dec 9th	9	1226.72		20.51
Dec 10th to Dec 31st	22	626.72			Payment of $600 (on Dec 10th)
			800.91		End of Billing Cycle
Jan 1st to Jan 9th	9	638.96		12.24
Jan 10th to Jan 31st	22	0			Payment of $638.96 (Jan 10th) to fully pay off balance
					End of Billing Cycle

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

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: $38.96
Silver Card interest charged: $45.41

Which card is better and by how much? The Gold Card is better by $6.45

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