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date\tamount ($)\ttransaction 4/1\t626.45\tbeginning balance 4/10\t37.4…

Question

date\tamount ($)\ttransaction
4/1\t626.45\tbeginning balance
4/10\t37.41\tpurchase
4/12\t44.50\tpurchase
5/3\t65.50\tpayment
5/16\t24.89\tpurchase
5/20\t104.77\tpayment
6/6\t23.60\tpayment
6/10\t15.00\tpurchase
6/14\t51.85\tpurchase
if adam’s credit card has an apr of 14.63%, what is adam’s balance at the end of june?
a. $629.42
b. $629.66
c. $627.27
d. $628.40

Explanation:

Step1: Calculate Average Daily Balance (ADB)

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

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

Now calculate the sum of (balance * days) for each period:

  • 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

Total sum = 5638.05 + 1327.72 + 14875.56 + 8357.18 + 2671.00 + 9570.66 + 2157.52 + 2217.52 + 10305.91 = 57121.16

Total days in the billing cycle (April to June): Let's check the days: 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days (Wait, actually, from 4/1 to 6/30: April has 30, May has 31, June has 30? Wait, no, let's recalculate the days correctly.

Wait, maybe a better way: The billing cycle is from 4/1 to 6/30. Let's list the days between each transaction:

  • 4/1 to 4/10: 9 days (4/1 - 4/9 is 9 days, 4/10 is the next day)
  • 4/10 to 4/12: 2 days (4/10, 4/11)
  • 4/12 to 5/3: 21 days (4/12 to 5/2 is 21 days, 5/3 is next)
  • 5/3 to 5/16: 13 days (5/3 to 5/15 is 13 days, 5/16 is next)
  • 5/16 to 5/20: 4 days (5/16 to 5/19 is 4 days, 5/20 is next)
  • 5/20 to 6/6: 17 days (5/20 to 6/5 is 17 days, 6/6 is next)
  • 6/6 to 6/10: 4 days (6/6 to 6/9 is 4 days, 6/10 is next)
  • 6/10 to 6/14: 4 days (6/10 to 6/13 is 4 days, 6/14 is next)
  • 6/14 to 6/30: 17 days (6/14 to 6/30 is 17 days)

Now sum the days: 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days (correct, April has 30, May 31, June 30; 30 + 31 + 30 = 91 days).

Now calculate the total of (balance * days):

  1. 626.45 * 9 = 5638.05
  2. 663.86 * 2 = 1327.72 (626.45 + 37.41 = 663.86)
  3. 708.36 * 21 = 14875.56 (663.86 + 44.50 = 708.36)
  4. 642.86 * 13 = 8357.18 (708.36 - 65.50 = 642.86)
  5. 667.75 * 4 = 2671.00 (642.86 + 24.89 = 667.75)
  6. 562.98 * 17 = 9570.66 (667.75 - 104.77 = 562.98)
  7. 539.38 * 4 = 2157.52 (562.98 - 23.60 = 539.38)
  8. 554.38 * 4 = 2217.52 (539.38 + 15.00 = 554.38)
  9. 606.23 * 17 = 10305.91 (554.38 + 51.85 = 606.23)

Sum these up: 5638.05 + 1327.72 = 6965.77; +14875.56 = 21841.33; +8357.18 = 30198.51; +2671.00 = 32869.51; +9570.66 = 42440.17; +2157.52 = 44597.69; +2217.52 = 46815.21; +10305.91 = 57121.12 (approx, slight difference due to rounding).

Average Daily Balance (ADB) = Total / 91 = 57121.12 / 91 ≈ 627.7046

Step2: Calculate Monthly Interest Rate

APR = 14.63%, so monthly rate (r) = 14.63% / 12 = 0.1463 / 12 ≈ 0.01219167

Step3: Calculate Finance Charge

Finance Charge = ADB r = 627.7046 0.01219167 ≈ 7.65

Step4: Calculate Ending Balance

First, find the balance before interest:

Let's track the balance step by step without interest first:

  • 4/1: 626.45
  • 4/10: +37.41 → 663.86
  • 4/12: +44.50 → 708.36
  • 5/3: -65.50 → 642.86
  • 5/16: +24.89 → 667.75
  • 5/20: -104.77 → 562.98
  • 6/6: -23.60 → 539.38
  • 6/10: +15.00 → 554.38
  • 6/14: +51.85 → 606.23

Now add the finance charge: 606.23 + 7.65 ≈ 613.88? Wait, that can't be right. Wait, maybe I made a mistake in the ADB calculation. Wait, no, the correct way is to calculate the ADB for the billing cycle (April to June), then add the finance cha…

Answer:

Step1: Calculate Average Daily Balance (ADB)

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

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

Now calculate the sum of (balance * days) for each period:

  • 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

Total sum = 5638.05 + 1327.72 + 14875.56 + 8357.18 + 2671.00 + 9570.66 + 2157.52 + 2217.52 + 10305.91 = 57121.16

Total days in the billing cycle (April to June): Let's check the days: 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days (Wait, actually, from 4/1 to 6/30: April has 30, May has 31, June has 30? Wait, no, let's recalculate the days correctly.

Wait, maybe a better way: The billing cycle is from 4/1 to 6/30. Let's list the days between each transaction:

  • 4/1 to 4/10: 9 days (4/1 - 4/9 is 9 days, 4/10 is the next day)
  • 4/10 to 4/12: 2 days (4/10, 4/11)
  • 4/12 to 5/3: 21 days (4/12 to 5/2 is 21 days, 5/3 is next)
  • 5/3 to 5/16: 13 days (5/3 to 5/15 is 13 days, 5/16 is next)
  • 5/16 to 5/20: 4 days (5/16 to 5/19 is 4 days, 5/20 is next)
  • 5/20 to 6/6: 17 days (5/20 to 6/5 is 17 days, 6/6 is next)
  • 6/6 to 6/10: 4 days (6/6 to 6/9 is 4 days, 6/10 is next)
  • 6/10 to 6/14: 4 days (6/10 to 6/13 is 4 days, 6/14 is next)
  • 6/14 to 6/30: 17 days (6/14 to 6/30 is 17 days)

Now sum the days: 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days (correct, April has 30, May 31, June 30; 30 + 31 + 30 = 91 days).

Now calculate the total of (balance * days):

  1. 626.45 * 9 = 5638.05
  2. 663.86 * 2 = 1327.72 (626.45 + 37.41 = 663.86)
  3. 708.36 * 21 = 14875.56 (663.86 + 44.50 = 708.36)
  4. 642.86 * 13 = 8357.18 (708.36 - 65.50 = 642.86)
  5. 667.75 * 4 = 2671.00 (642.86 + 24.89 = 667.75)
  6. 562.98 * 17 = 9570.66 (667.75 - 104.77 = 562.98)
  7. 539.38 * 4 = 2157.52 (562.98 - 23.60 = 539.38)
  8. 554.38 * 4 = 2217.52 (539.38 + 15.00 = 554.38)
  9. 606.23 * 17 = 10305.91 (554.38 + 51.85 = 606.23)

Sum these up: 5638.05 + 1327.72 = 6965.77; +14875.56 = 21841.33; +8357.18 = 30198.51; +2671.00 = 32869.51; +9570.66 = 42440.17; +2157.52 = 44597.69; +2217.52 = 46815.21; +10305.91 = 57121.12 (approx, slight difference due to rounding).

Average Daily Balance (ADB) = Total / 91 = 57121.12 / 91 ≈ 627.7046

Step2: Calculate Monthly Interest Rate

APR = 14.63%, so monthly rate (r) = 14.63% / 12 = 0.1463 / 12 ≈ 0.01219167

Step3: Calculate Finance Charge

Finance Charge = ADB r = 627.7046 0.01219167 ≈ 7.65

Step4: Calculate Ending Balance

First, find the balance before interest:

Let's track the balance step by step without interest first:

  • 4/1: 626.45
  • 4/10: +37.41 → 663.86
  • 4/12: +44.50 → 708.36
  • 5/3: -65.50 → 642.86
  • 5/16: +24.89 → 667.75
  • 5/20: -104.77 → 562.98
  • 6/6: -23.60 → 539.38
  • 6/10: +15.00 → 554.38
  • 6/14: +51.85 → 606.23

Now add the finance charge: 606.23 + 7.65 ≈ 613.88? Wait, that can't be right. Wait, maybe I made a mistake in the ADB calculation. Wait, no, the correct way is to calculate the ADB for the billing cycle (April to June), then add the finance charge to the balance before interest? Wait, no, the ending balance is the balance before interest plus the finance charge. Wait, let's recalculate the ADB correctly.

Wait, maybe the billing cycle is from April to June, so the transactions are:

Wait, another approach: The average daily balance method for credit cards: the balance is adjusted for each transaction, and we calculate the balance each day, sum them up, divide by number of days, then apply interest.

Wait, let's list all days from 4/1 to 6/30 (91 days) and track the balance each day:

Day 1 (4/1): 626.45

Days 2-9 (8 more days, total 9 days): 626.45 (days 1-9: 9 days)

Day 10 (4/10): 626.45 + 37.41 = 663.86

Day 11 (4/11): 663.86 (days 10-11: 2 days)

Day 12 (4/12): 663.86 + 44.50 = 708.36

Days 13-32 (20 more days, total 21 days: 12-32): 708.36 (days 12-32: 21 days)

Day 33 (5/3): 708.36 - 65.50 = 642.86

Days 34-45 (12 more days, total 13 days: 33-45): 642.86 (days 33-45: 13 days)

Day 46 (5/16): 642.86 + 24.89 = 667.75

Days 47-49 (3 more days, total 4 days: 46-49): 667.75 (days 46-49: 4 days)

Day 50 (5/20): 667.75 - 104.77 = 562.98

Days 51-66 (16 more days, total 17 days: 50-66): 562.98 (days 50-66: 17 days)

Day 67 (6/6): 562.98 - 23.60 = 539.38

Days 68-70 (3 more days, total 4 days: 67-70): 539.38 (days 67-70: 4 days)

Day 71 (6/10): 539.38 + 15.00 = 554.38

Days 72-74 (3 more days, total 4 days: 71-74): 554.38 (days 71-74: 4 days)

Day 75 (6/14): 554.38 + 51.85 = 606.23

Days 75-91 (17 days: 75-91): 606.23 (days 75-91: 17 days)

Now calculate the sum of balances:

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

Total sum = 5638.05 + 1327.72 + 14875.56 + 8357.18 + 2671.00 + 9570.66 + 2157.52 + 2217.52 + 10305.91 = 57121.12 (same as before)

ADB = 57121.12 / 91 ≈ 627.7046

Monthly interest rate: 14.63% / 12 = 0.1463 / 12 ≈ 0.01219167

Finance charge = 627.7046 * 0.01219167 ≈ 7.65

Now, the balance before interest is the balance on 6/30 before interest: 606.23 (from 6/14 transaction)

Then, ending balance = 606.23 + 7.65 ≈ 613.88? But the options are 629.42, 629.66, 627.27, 628.40. So I must have made a mistake in the ADB period.

Wait, maybe the billing cycle is from April to May to June, but maybe the transactions are:

Wait, let's check the dates again:

  • 4/1: beginning balance
  • 4/10: purchase
  • 4/12: purchase
  • 5/3: payment
  • 5/16: purchase
  • 5/20: payment
  • 6/6: payment
  • 6/10: purchase
  • 6/14: purchase

So the billing cycle is probably from April to June, so the days between transactions:

Wait, another way: the average daily balance is calculated by taking the balance each day, adding them up, dividing by the number of days in the billing cycle (91 days), then multiplying by the monthly interest rate to get the finance charge, then adding that to the balance before interest.

Wait, maybe my mistake is in the balance tracking. Let's track the balance step by step with each transaction:

  1. 4/1: 626.45 (day 1)
  2. 4/10: +37.41 → 663.86 (day 10)
  3. 4/12: +44.50 → 708.36 (day 12)
  4. 5/3: -65.50 → 642.86 (day 33)
  5. 5/16: +24.89 → 667.75 (day 46)
  6. 5/20: -104.77 → 562.98 (day 50)
  7. 6/6: -23.60 → 539.38 (day 67)
  8. 6/10: +15.00 → 554.38 (day 71)
  9. 6/14: +51.85 → 606.23 (day 75)

Now, the number of days for each balance:

  • 4/1 - 4/9: 9 days (days 1-9): balance 626.45
  • 4/10