date | amount ($) | transaction\n4/1 | 626.45 | beginning balance\n4/10 | 37.41 | purchase\n4/12 | 44.50 |…

date | amount ($) | transaction\n4/1 | 626.45 | beginning balance\n4/10 | 37.41 | purchase\n4/12 | 44.50 | purchase\n5/3 | 65.50 | payment\n5/16 | 24.89 | purchase\n5/20 | 104.77 | payment\n6/6 | 23.60 | payment\n6/10 | 15.00 | purchase\n6/14 | 51.85 | purchase\nif adams credit card has an apr of 14.63%, what is adams balance at the end of june?\na. $629.42\nb. $629.66\nc. $627.27\nd. $628.40

date | amount ($) | transaction\n4/1 | 626.45 | beginning balance\n4/10 | 37.41 | purchase\n4/12 | 44.50 | purchase\n5/3 | 65.50 | payment\n5/16 | 24.89 | purchase\n5/20 | 104.77 | payment\n6/6 | 23.60 | payment\n6/10 | 15.00 | purchase\n6/14 | 51.85 | purchase\nif adams credit card has an apr of 14.63%, what is adams balance at the end of june?\na. $629.42\nb. $629.66\nc. $627.27\nd. $628.40

Answer

Explanation:

Step1: Calculate the average daily balance (ADB)

First, we need to determine the number of days each balance is held.

  • From 4/1 to 4/9 (9 days): Balance = $626.45
  • From 4/10 to 4/11 (2 days): Balance = $626.45 + $37.41 = $663.86
  • From 4/12 to 5/2 (21 days): Balance = $663.86 + $44.50 = $708.36
  • From 5/3 to 5/15 (13 days): Balance = $708.36 - $65.50 = $642.86
  • From 5/16 to 5/19 (4 days): Balance = $642.86 + $24.89 = $667.75
  • From 5/20 to 6/5 (17 days): Balance = $667.75 - $104.77 = $562.98
  • From 6/6 to 6/9 (4 days): Balance = $562.98 - $23.60 = $539.38
  • From 6/10 to 6/13 (4 days): Balance = $539.38 + $15.00 = $554.38
  • From 6/14 to 6/30 (17 days): Balance = $554.38 + $51.85 = $606.23

Now, calculate the sum of (balance × number of days):

  • $626.45 × 9 = $5638.05
  • $663.86 × 2 = $1327.72
  • $708.36 × 21 = $14875.56
  • $642.86 × 13 = $8357.18
  • $667.75 × 4 = $2671.00
  • $562.98 × 17 = $9570.66
  • $539.38 × 4 = $2157.52
  • $554.38 × 4 = $2217.52
  • $606.23 × 17 = $10305.91

Sum these up: $5638.05 + $1327.72 + $14875.56 + $8357.18 + $2671.00 + $9570.66 + $2157.52 + $2217.52 + $10305.91 = $56121.12

Number of days in the period (from 4/1 to 6/30): 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days

ADB = $\frac{56121.12}{91}$ ≈ $616.7156$

Step2: Calculate the monthly interest rate

APR = 14.63%, so monthly rate (r) = $\frac{0.1463}{12}$ ≈ 0.0121917

Step3: Calculate the interest

Interest = ADB × r ≈ $616.7156 × 0.0121917 ≈ $7.52

Step4: Calculate the ending balance

First, find the balance before interest (sum of all transactions): Beginning balance: $626.45 Purchases: $37.41 + $44.50 + $24.89 + $15.00 + $51.85 = $173.65 Payments: $65.50 + $104.77 + $23.60 = $193.87 Balance before interest = $626.45 + $173.65 - $193.87 = $606.23 (matches the last balance before interest)

Now, add the interest: $606.23 + $7.52 = $613.75? Wait, no, wait. Wait, the ADB method: the ending balance is (balance before interest) + interest? Wait, no, the correct formula for credit card balance with ADB is:

Ending balance = (ADB × (1 + r)) + (final balance before interest - ADB)? Wait, no, actually, the ADB is used to calculate the interest, then the ending balance is the balance before interest (after all transactions) plus the interest.

Wait, let's recalculate the balance before interest correctly:

Beginning balance: $626.45

4/10: +$37.41 → $663.86 (9 days later, 4/10)

4/12: +$44.50 → $708.36 (21 days later, 5/2)

5/3: -$65.50 → $642.86 (13 days later, 5/15)

5/16: +$24.89 → $667.75 (4 days later, 5/19)

5/20: -$104.77 → $562.98 (17 days later, 6/5)

6/6: -$23.60 → $539.38 (4 days later, 6/9)

6/10: +$15.00 → $554.38 (4 days later, 6/13)

6/14: +$51.85 → $606.23 (17 days later, 6/30)

So the balance before interest on 6/30 is $606.23.

Now, calculate interest using ADB:

ADB = $\frac{\sum (balance × days)}{\sum days}$ = $\frac{56121.12}{91}$ ≈ $616.7156$

Interest = $616.7156 × \frac{0.1463}{12}$ ≈ $616.7156 × 0.0121917 ≈ $7.52

Then, ending balance = balance before interest + interest = $606.23 + $7.52 = $613.75? Wait, that's not matching the options. Wait, maybe I made a mistake in the days calculation.

Wait, let's recheck the days:

  • 4/1 to 4/9: 9 days (April has 30 days, so 30 - 1 + 1? Wait, no, 4/1 is day 1, 4/10 is day 10, so from 4/1 to 4/9 is 9 days (inclusive? No, exclusive? Wait, the number of days between 4/1 and 4/10 is 9 days (4/1 to 4/9 is 9 days, then 4/10 is the next day). So:

  • 4/1 - 4/9: 9 days (balance $626.45)

  • 4/10 - 4/11: 2 days (balance $626.45 + 37.41 = $663.86)

  • 4/12 - 5/2: from 4/12 to 5/2. April has 30 days, so 30 - 12 + 1 = 19 days in April, plus 2 days in May: 19 + 2 = 21 days. Correct.

  • 5/3 - 5/15: 15 - 3 + 1 = 13 days. Correct.

  • 5/16 - 5/19: 19 - 16 + 1 = 4 days. Correct.

  • 5/20 - 6/5: May has 31 days, so 31 - 20 + 1 = 12 days in May, plus 5 days in June: 12 + 5 = 17 days. Correct.

  • 6/6 - 6/9: 9 - 6 + 1 = 4 days. Correct.

  • 6/10 - 6/13: 13 - 10 + 1 = 4 days. Correct.

  • 6/14 - 6/30: 30 - 14 + 1 = 17 days. Correct.

Total days: 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days. Correct.

Sum of (balance × days):

  • 4/1 - 4/9: 626.45 × 9 = 5638.05
  • 4/10 - 4/11: 663.86 × 2 = 1327.72 (total 5638.05 + 1327.72 = 6965.77)
  • 4/12 - 5/2: 708.36 × 21 = 14875.56 (total 6965.77 + 14875.56 = 21841.33)
  • 5/3 - 5/15: 642.86 × 13 = 8357.18 (total 21841.33 + 8357.18 = 30198.51)
  • 5/16 - 5/19: 667.75 × 4 = 2671.00 (total 30198.51 + 2671.00 = 32869.51)
  • 5/20 - 6/5: 562.98 × 17 = 9570.66 (total 32869.51 + 9570.66 = 42440.17)
  • 6/6 - 6/9: 539.38 × 4 = 2157.52 (total 42440.17 + 2157.52 = 44597.69)
  • 6/10 - 6/13: 554.38 × 4 = 2217.52 (total 44597.69 + 2217.52 = 46815.21)
  • 6/14 - 6/30: 606.23 × 17 = 10305.91 (total 46815.21 + 10305.91 = 57121.12) Wait, earlier I had 56121.12, that was a mistake! 57121.12, not 56121.12.

So ADB = 57121.12 / 91 ≈ 627.7046

Now, monthly rate: 0.1463 / 12 ≈ 0.0121917

Interest = 627.7046 × 0.0121917 ≈ 7.65

Now, balance before interest: 626.45 (beginning) + 37.41 + 44.50 + 24.89 + 15.00 + 51.85 (purchases) - 65.50 - 104.77 - 23.60 (payments)

Purchases total: 37.41 + 44.50 = 81.91; 81.91 + 24.89 = 106.8; 106.8 + 15.00 = 121.8; 121.8 + 51.85 = 173.65

Payments total: 65.50 + 104.77 = 170.27; 170.27 + 23.60 = 193.87

Balance before interest: 626.45 + 173.65 - 193.87 = 626.45 + 173.65 = 800.1; 800.1 - 193.87 = 606.23. Wait, that's still 606.23. Wait, no, the ADB is the average daily balance, which is used to calculate interest, then the ending balance is balance before interest + interest? No, wait, the correct formula for credit card balance with ADB is:

Ending balance = (ADB × (1 + r)) + (final balance before interest - ADB)? No, no. The ADB is used to calculate the interest, then the ending balance is the balance after all transactions (before interest) plus the interest. Wait, no, the interest is added to the ADB? No, the ADB is the average balance, so the interest is ADB × monthly rate, then the ending balance is (balance before interest) + interest? Wait, no, the balance before interest is the balance on the last day, but the interest is calculated on the average daily balance. So the ending balance is (balance before interest) + interest? No, that's not right. Wait, the correct process is:

  1. Calculate ADB (average daily balance) over the billing cycle.
  2. Calculate interest: ADB × (APR / 12)
  3. Ending balance = (balance before interest) + interest

Wait, balance before interest is the balance after all transactions (purchases and payments) on the last day. In this case, the last day is 6/30, balance is $606.23.

Then, interest is ADB × (0.1463 / 12) ≈ 627.7046 × 0.0121917 ≈ 7.65

So ending balance = 606.23 + 7.65 ≈ 613.88. But this is not matching the options. Wait, maybe the billing cycle is from 4/1 to 6/30, so the number of days is 91, but maybe the APR is applied to the ADB for the month, and the ending balance is ADB × (1 + APR/12). Wait, let's try that:

ADB ≈ 627.7046

Ending balance = 627.7046 × (1 + 0.1463/12) ≈ 627.7046 × 1.0121917 ≈ 627.7046 + 7.65 ≈ 635.35. No, still not.

Wait, maybe I made a mistake in the balance calculations. Let's recalculate the balances step by step:

  • 4/1: $626.45 (beginning balance)
  • 4/10: +$37.41 → $626.45 + 37.41 = $663.86 (days 4/1-4/9: 9 days, balance $626.45; 4/10-4/11: 2 days, balance $663.86)
  • 4/12: +$44.50 → $663.86 + 44.50 = $708.36 (days 4/12-5/2: 21 days, balance $708.36)
  • 5/3: -$65.50 → $708.36 - 65.50 = $642.86 (days 5/3-5/15: 13 days, balance $642.86)
  • 5/16: +$24.89 → $642.86 + 24.89 = $667.75 (days 5/16-5/19: 4 days, balance $667.75)
  • 5/20: -$104.77 → $667.75 - 104.77 = $562.98 (days 5/20-6/5: 17 days, balance $562.98)
  • 6/