Tuesday, November 17, 2015

Question Four: How Long Does It Take to Pay Off Credit Card Debt

Question Four:  A person has $15,000 in credit card debt divided over 5 credit cards with identical terms.   The interest rate on all five cards is 12%.  The minimum required monthly payment is 3.0% of the monthly balance.  

How long would it take for the person to repay the entire $15,000 in credit card debt if the person continues to pay 3.0% of  $15,000?

How long would it take for the person to cut the loan balance in half if the person continues to make this monthly payment?




Answer:   We have the interest rate, the initial loan balance, and the payment but we do not have the term of the loan.   The actual amount that we will pay per month is $450 (3.0 percent of $15,000.)   We can insert the interest rate (monthly of course) and the loan balance with different estimates of the term in the PMT function.    The actual repayment period is the term that gives us a value of the PMT function equal to the actual monthly payment of $450.

At 40 months the PMT function tells us the required payment is $456.    At 41 months the payment function gives us a payment of $447.77.

The loan will be completely repaid on payment 41.

This result can be confirmed by observing that the future value of the loan becomes $0 at somewhere between 40 and 41 months.

The credit card balance is obtained from the FV function.   The final chart reveals that the credit card balance has fallen by 50% on the 23rd monthly payment.











Payment by Term for $15,000 balance at 12% Interest
Payment at 12 % Interest Rate
Payment Term
Credit Card Balance
Note
-$1,332.73
12
$15,000
-$706.10
24
$15,000
-$498.21
36
$15,000
-$395.01
48
$15,000
-$333.67
60
$15,000
-$293.25
72
$15,000
-$264.79
84
$15,000
-$243.79
96
$15,000
$15,000
$15,000
-$498.21
36
$15,000
-$487.02
37
$15,000
-$476.42
38
$15,000
-$466.37
39
$15,000
-$456.83
40
$15,000
-$447.77
41
$15,000
Payment <= $450 at 12 %
-$439.13
42
$15,000
-$430.91
43
$15,000
-$423.07
44
$15,000
-$415.58
45
$15,000
-$408.42
46
$15,000
-$401.57
47
$15,000

Somewhere between 40 and 41 months the payment on the loan is $450 the required minimum monthly payment in this problem.





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