Question

Many people choose to pay minimum payment on their credit card. Suppose you owe 1000 on a credit card with a 10% interest rate, and a minimum payment of $10 or 2% of the balance, which ever is greater. How soon will you pay off this debt if you make the minimum payment each month? How much total interest will you pay? If you pay equal amount each month in 10 years, how much will you pay in total? Which method pays more? What if the interest rate is 6% per year. Which recommendation will you give?

Answer 1

a) Method-1:

Minimun monthly payment = Greater of $10 or 20% of $1000 = $20

Interest per month = Balance at beginning x 10% / 12

outstanding Balance at the end = Balance at beginning + Interest per month - Minimun Payment

So, It would take 65months to clear debt and you will pay interest of $298.98

b) Method-2:

Calculation of Equated Monthly Installment(EMI):

An equated monthly installment (EMI) is a fixed payment amount made by a borrower to a lender at a specified date each calendar month.

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

Where,

• E – EMI
• P – Principal Loan Amount
• r – Rate of interest calculated on monthly basis.
• n – Loan term in Years / Months (Divide by 12 for Months)

EMI calculation using excel:

=PMT (rate, nper, pv, [fv], [type]

Where,

• Rate:     Interest Rate per period
• Nper:    The number of periods
• Pv:         Present value of loan/investment
• Fv:         Future value of the loan/investment – This is optional. If left blank, it will default to zero.
• Type:     Defines if the payment is made at the start or end of the period. If left blank, defaults to zero.

              0 – Payment is made at the end of the period
             1 – Payment is made at the beginning of the period

Calculation of EMI sing Excel formula:

=pmt(10%/12, 10x12, $1000)

EMI = $13.22

If you pay $13.22 per month till 10 years then you will pay interest $585.39.

So, Total Payment will be $1000+$585.39 = $1585.39

Comparing method-1 and metgod-2, In method-2 you will pay more interest then method-1. i.e If you choose to pay eqaul amount of $13.22 per month over the 10 years then it will be more costlier the minimun payment of $20 per month.

c) Calculation is interest is 6%.

Method-1 : Minimum Payment of $20

So, It would take 58months to clear debt and you will pay interest of $253.61

Method-2:

Calculation of EMI sing Excel formula:

=pmt(6%/12, 10x12, $1000)

EMI = $11.10

If you pay $11.10 per month till 10 years then you will pay interest $332.24.

So, Total Payment will be $1000+$332.24 = $1332.24

Comparing method-1 and metgod-2, In method-2 you will pay more interest then method-1. i.e If you choose to pay eqaul amount of $11.10 per month over the 10 years then it will be more costlier the minimun payment of $20 per month.

Whatever interest rate is there either 10% or 6% but Method-1 is more beneficial then method-2 because in method-1 yo will pay minimum payment of $20 which is higher then EMI of method-2 and it reduce your interest cost.