Question 1173028: On October 23, 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.)
Based on this information, calculate the interest (in $) charged by each card for this purchase.
Silver card: $_____
Gold card: $______
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's calculate the interest charged by each card.
**Silver Card (18% interest, balance on the first day of the previous month):**
* **October:**
* Balance on October 1st: $0
* Purchase on October 23rd: $1,800
* Interest for October: $0 (since the balance on Oct 1 was 0)
* **November:**
* Balance on November 1st: $1,800
* Interest for November: $1,800 * (0.18 / 12) = $27
* Payment on November 10th: $600
* Remaining balance: $1,800 + $27 - $600 = $1,227
* **December:**
* Balance on December 1st: $1,227
* Interest for December: $1,227 * (0.18 / 12) = $18.41
* Payment on December 10th: $600
* Remaining balance: $1,227 + $18.41 - $600 = $645.41
* **January:**
* Balance on January 1st: $645.41
* Interest for January: $645.41 * (0.18 / 12) = $9.68
* Payment on January 10th: $645.41+$9.68 = $655.09
* **Total Interest (Silver Card):** $27 + $18.41 + $9.68 = $55.09
**Gold Card (18% interest, average daily balance):**
* **October:**
* Days with $0 balance: 22
* Days with $1,800 balance: 8 (including Oct 23rd)
* Average daily balance: [(22 * $0) + (8 * $1,800)] / 30 = $1,440
* Interest for October: $1,440 * (0.18 / 12) = $21.60
* **November:**
* Balance at the start of Nov: $1,800 + $21.60 = $1,821.60
* Days with 1821.60 balance: 9.
* Balance after payment: $1,821.60 - $600 = $1,221.60.
* Days with 1221.60 balance: 21
* Average daily balance: [(9 * $1,821.60) + (21 * $1,221.60)] / 30 = $1,401.60
* Interest for November: $1,401.60 * (0.18 / 12) = $21.02
* **December:**
* Balance at the start of Dec: $1,221.60 + $21.02 = $1,242.62
* Days with 1242.62 balance: 9.
* Balance after payment: $1,242.62 - $600 = $642.62
* Days with $642.62 balance: 21
* Average daily balance: [(9 * $1,242.62) + (21 * $642.62)] / 30 = $822.62
* Interest for December: $822.62 * (0.18 / 12) = $12.34
* **January:**
* Balance at start of January: $642.62 + $12.34 = $654.96
* Days with 654.96 balance: 10.
* Average daily balance: $654.96
* Interest for January: $654.96 * (0.18 / 12) = $9.82
* **Total Interest (Gold Card):** $21.60 + $21.02 + $12.34 + $9.82 = $64.78
**Answers:**
* Silver card: $55.09
* Gold card: $64.78
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