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 23^{rd} 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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