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QUESTION IMAGE

date | amount ($) | transaction 4/1 | 626.45 | beginning balance 4/10 |…

Question

date | amount ($) | transaction
4/1 | 626.45 | beginning balance
4/10 | 37.41 | purchase
4/12 | 44.50 | purchase
5/3 | 65.50 | payment
5/16 | 24.89 | purchase
5/20 | 104.77 | payment
6/6 | 23.60 | payment
6/10 | 15.00 | purchase
6/14 | 51.85 | purchase
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

Sum these up: 5638.05 + 1327.72 + 14875.56 + 8357.18 + 2671.00 + 9570.66 + 2157.52 + 2217.52 + 10305.91 = 57121.12

Total days in the billing cycle (April to June): 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days

ADB = 57121.12 / 91 ≈ 627.70 (Wait, maybe I made a mistake in day counts. Let's re - calculate the number of days correctly.

Alternative approach for day counts (from April 1 to June 30):

April has 30 days, May has 31 days, June has 30 days.

  • 4/1 - 4/9: 9 days (April 1 - April 9)
  • 4/10 - 4/11: 2 days (April 10 - April 11)
  • 4/12 - 4/30: 30 - 12 + 1 = 19 days? Wait, my previous day count was wrong. Let's use the correct way:

Start over with correct day intervals:

  1. 4/1: beginning balance. So from 4/1 to 4/9 (inclusive), that's 9 days (April 1 - April 9: 9 days)
  2. 4/10: purchase. From 4/10 to 4/11: 2 days (April 10 - April 11)
  3. 4/12: purchase. From 4/12 to 5/2: April has 30 days, so 30 - 12 + 1 = 19 days? Wait, 4/12 to 5/2: 30 - 12 + 1 + 2? No, 4/12 to 4/30 is 30 - 12 = 18 days (since 4/12 is day 0, 4/13 is day 1,..., 4/30 is day 18), then 5/1 and 5/2: 2 days. So total 18 + 2 = 20 days? I think my initial day count was incorrect. Let's use the method of calculating the number of days between two dates.

The correct way is to calculate the number of days each balance is active:

  • 4/1 - 4/9: 9 days (April 1 to April 9)
  • 4/10 - 4/11: 2 days (April 10 to April 11)
  • 4/12 - 5/2: 30 - 12 + 1+2? Wait, April has 30 days. 4/12 to 4/30: 30 - 12 = 18 days (because 4/12 is day 0, 4/13 is day 1, so 4/30 is day 18). Then 5/1 and 5/2: 2 days. So 18 + 2 = 20 days.
  • 5/3 - 5/15: 15 - 3 + 1 = 13 days (May 3 to May 15)
  • 5/16 - 5/19: 19 - 16 + 1 = 4 days (May 16 to May 19)
  • 5/20 - 6/5: 31 - 20 + 1+5 = 17 days (May 20 to May 31: 12 days, June 1 - June 5: 5 days; 12 + 5 = 17)
  • 6/6 - 6/9: 9 - 6 + 1 = 4 days (June 6 to June 9)
  • 6/10 - 6/13: 13 - 10 + 1 = 4 days (June 10 to June 13)
  • 6/14 - 6/30: 30 - 14 + 1 = 17 days (June 14 to June 30)

Now recalculate the balances and (balance × days):

  1. 4/1 - 4/9: balance = 626.45, days = 9, product = 626.45×9 = 5638.05
  2. 4/10 - 4/11: balance = 626.45 + 37.41 = 663.86, days = 2, product = 663.86×2 = 1327.72
  3. 4/12 - 5/2: balance = 663.86 + 44.50 = 708.36, days = 20, product = 708.36×20 = 14167.2
  4. 5/3 - 5/15: balance = 708.36 - 65.50 = 642.86, days = 13, product = 642.86×13 = 8357.18
  5. 5/16 - 5/19: balance = 642.86 + 24.89 = 667.75, days = 4, product = 667.75×4 = 2671
  6. 5/20 - 6/5: balance = 667.75 - 104.77 = 562.98, days = 17, product = 562.98×17 = 9570.66
  7. 6/6 - 6/9: balance = 562.98 - 23.60 = 539.38, days = 4, product = 539.38×4 = 2157.52
  8. 6/10 - 6/13: balance = 539.38 + 15.00 = 554.38, days = 4, produc…

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

Sum these up: 5638.05 + 1327.72 + 14875.56 + 8357.18 + 2671.00 + 9570.66 + 2157.52 + 2217.52 + 10305.91 = 57121.12

Total days in the billing cycle (April to June): 9 + 2 + 21 + 13 + 4 + 17 + 4 + 4 + 17 = 91 days

ADB = 57121.12 / 91 ≈ 627.70 (Wait, maybe I made a mistake in day counts. Let's re - calculate the number of days correctly.

Alternative approach for day counts (from April 1 to June 30):

April has 30 days, May has 31 days, June has 30 days.

  • 4/1 - 4/9: 9 days (April 1 - April 9)
  • 4/10 - 4/11: 2 days (April 10 - April 11)
  • 4/12 - 4/30: 30 - 12 + 1 = 19 days? Wait, my previous day count was wrong. Let's use the correct way:

Start over with correct day intervals:

  1. 4/1: beginning balance. So from 4/1 to 4/9 (inclusive), that's 9 days (April 1 - April 9: 9 days)
  2. 4/10: purchase. From 4/10 to 4/11: 2 days (April 10 - April 11)
  3. 4/12: purchase. From 4/12 to 5/2: April has 30 days, so 30 - 12 + 1 = 19 days? Wait, 4/12 to 5/2: 30 - 12 + 1 + 2? No, 4/12 to 4/30 is 30 - 12 = 18 days (since 4/12 is day 0, 4/13 is day 1,..., 4/30 is day 18), then 5/1 and 5/2: 2 days. So total 18 + 2 = 20 days? I think my initial day count was incorrect. Let's use the method of calculating the number of days between two dates.

The correct way is to calculate the number of days each balance is active:

  • 4/1 - 4/9: 9 days (April 1 to April 9)
  • 4/10 - 4/11: 2 days (April 10 to April 11)
  • 4/12 - 5/2: 30 - 12 + 1+2? Wait, April has 30 days. 4/12 to 4/30: 30 - 12 = 18 days (because 4/12 is day 0, 4/13 is day 1, so 4/30 is day 18). Then 5/1 and 5/2: 2 days. So 18 + 2 = 20 days.
  • 5/3 - 5/15: 15 - 3 + 1 = 13 days (May 3 to May 15)
  • 5/16 - 5/19: 19 - 16 + 1 = 4 days (May 16 to May 19)
  • 5/20 - 6/5: 31 - 20 + 1+5 = 17 days (May 20 to May 31: 12 days, June 1 - June 5: 5 days; 12 + 5 = 17)
  • 6/6 - 6/9: 9 - 6 + 1 = 4 days (June 6 to June 9)
  • 6/10 - 6/13: 13 - 10 + 1 = 4 days (June 10 to June 13)
  • 6/14 - 6/30: 30 - 14 + 1 = 17 days (June 14 to June 30)

Now recalculate the balances and (balance × days):

  1. 4/1 - 4/9: balance = 626.45, days = 9, product = 626.45×9 = 5638.05
  2. 4/10 - 4/11: balance = 626.45 + 37.41 = 663.86, days = 2, product = 663.86×2 = 1327.72
  3. 4/12 - 5/2: balance = 663.86 + 44.50 = 708.36, days = 20, product = 708.36×20 = 14167.2
  4. 5/3 - 5/15: balance = 708.36 - 65.50 = 642.86, days = 13, product = 642.86×13 = 8357.18
  5. 5/16 - 5/19: balance = 642.86 + 24.89 = 667.75, days = 4, product = 667.75×4 = 2671
  6. 5/20 - 6/5: balance = 667.75 - 104.77 = 562.98, days = 17, product = 562.98×17 = 9570.66
  7. 6/6 - 6/9: balance = 562.98 - 23.60 = 539.38, days = 4, product = 539.38×4 = 2157.52
  8. 6/10 - 6/13: balance = 539.38 + 15.00 = 554.38, days = 4, product = 554.38×4 = 2217.52
  9. 6/14 - 6/30: balance = 554.38 + 51.85 = 606.23, days = 17, product = 606.23×17 = 10305.91

Now sum all the products:
5638.05 + 1327.72 + 14167.2 + 8357.18 + 2671 + 9570.66 + 2157.52 + 2217.52 + 10305.91

Let's add step by step:
5638.05 + 1327.72 = 6965.77
6965.77 + 14167.2 = 21132.97
21132.97 + 8357.18 = 29490.15
29490.15 + 2671 = 32161.15
32161.15 + 9570.66 = 41731.81
41731.81 + 2157.52 = 43889.33
43889.33 + 2217.52 = 46106.85
46106.85 + 10305.91 = 56412.76

Total days = 9 + 2 + 20 + 13 + 4 + 17 + 4 + 4 + 17 = 90 days (Wait, 9+2=11, 11+20=31, 31+13=44, 44+4=48, 48+17=65, 65+4=69, 69+4=73, 73+17=90)

ADB = 56412.76 / 90 ≈ 626.81 (Still not matching, maybe my day count is still wrong. Let's use the standard method for credit card average daily balance: the number of days in the billing cycle. Let's assume the billing cycle is from April 1 to June 30, which is 91 days (April:30, May:31, June:30; 30+31+30=91).

Let's list all the transactions with their post - balance and the number of days each balance is maintained:

  • April 1: balance = 626.45. Days until next transaction (April 10): 10 - 1 = 9 days (April 1 - April 9)
  • April 10: purchase, new balance = 626.45 + 37.41 = 663.86. Days until next transaction (April 12): 12 - 10 = 2 days (April 10 - April 11)
  • April 12: purchase, new balance = 663.86 + 44.50 = 708.36. Days until next transaction (May 3): 30 - 12 + 3 = 21 days? Wait, April has 30 days, so from April 12 to April 30: 30 - 12 = 18 days, and May 1 - May 2: 2 days. Total 18 + 2 = 20 days? No, May 3 is the next transaction, so from April 12 to May 2: 30 - 12 + 2 = 20 days (April 12 - April 30: 18 days, May 1 - May 2: 2 days), then May 3 is the transaction day. So days for balance 708.36: 20 days.
  • May 3: payment, new balance = 708.36 - 65.50 = 642.86. Days until next transaction (May 16): 16 - 3 = 13 days (May 3 - May 15)
  • May 16: purchase, new balance = 642.86 + 24.89 = 667.75. Days until next transaction (May 20): 20 - 16 = 4 days (May 16 - May 19)
  • May 20: payment, new balance = 667.75 - 104.77 = 562.98. Days until next transaction (June 6): 31 - 20 + 6 = 17 days (May 20 - May 31: 11 days, June 1 - June 5: 5 days; 11 + 5 = 16? Wait, May 20 to June 5: May has 31 days, so 31 - 20 + 5 = 16 days? No, June 6 is the transaction day, so from May 20 to June 5: 31 - 20 + 5 = 16 days (May 20 - May 31: 11 days, June 1 - June 5: 5 days), then June 6 is the transaction day. So days for balance 562.98: 16 days?
  • June 6: payment, new balance = 562.98 - 23.60 = 539.38. Days until next transaction (June 10): 10 - 6 = 4 days (June 6 - June 9)
  • June 10: purchase, new balance = 539.38 + 15.00 = 554.38. Days until next transaction (June 14): 14 - 10 = 4 days (June 10 - June 13)
  • June 14: purchase, new balance = 554.38 + 51.85 = 606.23. Days until end of June (June 30): 30 - 14 = 16 days? Wait, June 14 to June 30: 30 - 14 = 16 days (June 14 - June 30), but June has 30 days, so 30 - 14 + 1 = 17 days (including June 14).

This is getting too complicated. Maybe a better way is to use the formula for average daily balance:

ADB = (sum of (daily balance)) / number of days in the cycle.

Let's list the daily balance for each day from April 1 to June 30 (91 days):

April 1 - 9: 9 days, balance = 626.45
April 10 - 11: 2 days, balance = 626.45 + 37.41 = 663.86
April 12 - May 2: 21 days (April 12 - April 30 is 19 days, May 1 - May 2 is 2 days; 19 + 2 = 21), balance = 663.86 + 44.50 = 708.36
May 3 - May 15: 13 days, balance = 708.36 - 65.50 = 642.86
May 16 - May 19: 4 days, balance = 642.86 + 24.89 = 667.75
May 20 - June 5: 17 days (May 20 - May 31 is 12 days, June 1 - June 5 is 5 days; 12 + 5 = 17), balance = 667.75 - 104.77 = 562.98
June 6 - June 9: 4 days,