An alternative to using logarithms to determine the amount of time that it would
ID: 2726658 • Letter: A
Question
An alternative to using logarithms to determine the amount of time that it would take to pay off a credit card would be to use a spreadsheet to list the value of the minimum payment after each paymenet period for as many times as is necessary.
Suppose that you “max out” a credit card to its limit of $10,000 and plan on paying off this $10,000 balance by making minimum payments of $250 (no other charges will be made with this card as you plan on destroying it once the balance is paid off). On the 8th day of each billing cycle, an automatic payment of $250 will be made to the credit card company which processes and records it on the same day as the payment.
At the end of each billing cycle the finance charge is added to the balance to create the beginning balance of the following billing cycle with an APR of 17.64%. Assuming that the average daily balance method is used and that the billing cycle is 30 days in length, determine how long it will take for the credit card to be completely paid off by showing the beginning balance of each billing cycle and each finance charge up to (and including) the one where the card is paid off.
To clarify, the card will be considered to be paid off when the amount owed at the time that the payment is scheduled to be made is $200 or less (essentially meaning that it will be paid off during the first billing cycle where the beginning balance is $200 or less).
Explanation / Answer
Answer: It would take 59 monthly installments to repay credit card limit of $10,000/-.Methodology to calculate is as follows:
Following components are required to calculate the term of repayment:
a] Average Daily Balance
b] Annual interest.
a] Average daily balance:
[(Opening balance*no. of days due) + (Opening balance-Repayment amount)*no. of days left]/Billing period
In this case:
Billing period=30 days
Average daily balance = [10000*8+(10000-250)*22]/30 = $9,817/-
b] Calculation of Interest:
APR = 17.64%
Monthly rate= 17.64%/12= 0.0147.
Monthly interest charge = Average daily balance*Monthly rate= 9,817*0.0147=144.31
Therefore opening balance would be Closing balance + Interest = 10000-250+144.31=9894.
Sr no. Opening Balance Installment Closing Balance Average daily Bal. Monthly Interest rate Monthly Interest 1 10,000 250 9,750 9,817 0.0147 144 2 9,894 250 9,644 9,711 0.0147 143 3 9,787 250 9,537 9,604 0.0147 141 4 9,678 250 9,428 9,495 0.0147 140 5 9,568 250 9,318 9,384 0.0147 138 6 9,456 250 9,206 9,272 0.0147 136 7 9,342 250 9,092 9,159 0.0147 135 8 9,227 250 8,977 9,043 0.0147 133 9 9,110 250 8,860 8,926 0.0147 131 10 8,991 250 8,741 8,808 0.0147 129 11 8,870 250 8,620 8,687 0.0147 128 12 8,748 250 8,498 8,565 0.0147 126 13 8,624 250 8,374 8,441 0.0147 124 14 8,498 250 8,248 8,315 0.0147 122 15 8,370 250 8,120 8,187 0.0147 120 16 8,241 250 7,991 8,057 0.0147 118 17 8,109 250 7,859 7,926 0.0147 117 18 7,976 250 7,726 7,792 0.0147 115 19 7,840 250 7,590 7,657 0.0147 113 20 7,703 250 7,453 7,519 0.0147 111 21 7,563 250 7,313 7,380 0.0147 108 22 7,422 250 7,172 7,238 0.0147 106 23 7,278 250 7,028 7,095 0.0147 104 24 7,132 250 6,882 6,949 0.0147 102 25 6,984 250 6,734 6,801 0.0147 100 26 6,834 250 6,584 6,651 0.0147 98 27 6,682 250 6,432 6,499 0.0147 96 28 6,528 250 6,278 6,344 0.0147 93 29 6,371 250 6,121 6,188 0.0147 91 30 6,212 250 5,962 6,029 0.0147 89 31 6,051 250 5,801 5,867 0.0147 86 32 5,887 250 5,637 5,704 0.0147 84 33 5,721 250 5,471 5,537 0.0147 81 34 5,552 250 5,302 5,369 0.0147 79 35 5,381 250 5,131 5,198 0.0147 76 36 5,207 250 4,957 5,024 0.0147 74 37 5,031 250 4,781 4,848 0.0147 71 38 4,853 250 4,603 4,669 0.0147 69 39 4,671 250 4,421 4,488 0.0147 66 40 4,487 250 4,237 4,304 0.0147 63 41 4,300 250 4,050 4,117 0.0147 61 42 4,111 250 3,861 3,928 0.0147 58 43 3,919 250 3,669 3,735 0.0147 55 44 3,724 250 3,474 3,540 0.0147 52 45 3,526 250 3,276 3,342 0.0147 49 46 3,325 250 3,075 3,141 0.0147 46 47 3,121 250 2,871 2,938 0.0147 43 48 2,914 250 2,664 2,731 0.0147 40 49 2,704 250 2,454 2,521 0.0147 37 50 2,491 250 2,241 2,308 0.0147 34 51 2,275 250 2,025 2,092 0.0147 31 52 2,056 250 1,806 1,873 0.0147 28 53 1,834 250 1,584 1,650 0.0147 24 54 1,608 250 1,358 1,424 0.0147 21 55 1,379 250 1,129 1,195 0.0147 18 56 1,146 250 896 963 0.0147 14 57 910 250 660 727 0.0147 11 58 671 250 421 488 0.0147 7 59 428 250 178 245 0.0147 4 60 182 250 -68 -1 0.0147 -0Related Questions
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