Question

Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost: You just received an offer in the mail to transfer your $12,000 balance from your current credit card, which charges an annual rate of 18.6 percent, to a new credit card charging a rate of 8.2 percent. How much faster could you pay the loan off by making your planned monthly payments of $250 with the new card? What if there was a 2 percent fee charged on any balances transferred?

Please show the full workings and formula.

Answer 1

We need to calculate the time required to repay the loan with the current credit card (@18.6% rate) and with a new card (@8.2% rate).

Case1: Repayment on old card with 18.6% annual interest rate

Since, the interest is charged monthly and the payments are made monthly, we need to convert the annual interest rate to a monthly interest rate and then calculate the number of months required to repay the loan. The calculation is shown below:

Particulars		Calculator	Comments
Yearly Interest Rate	18.60%
Monthly Interest Rate	1.55%	I/Y	Converted to monthly
Monthly Payment	250	PMT	Payment made
Loan Outstanding	12000	PV	Card Balance Outstanding
Future Value	0.00	FV	Complete Repayment
Repayment Tenor	88.59	N	Months required to repay

Using Calculator: The notations have been given above. Enter the values in the scond column in the notations given in third column and calculate 'N" accordingly.

Using Excel: Use the NPER formula as: = NPER (1.55%, 250, -12000, 0 ,0)

Hence, on the existing card, the loan can be repaid in approximately 89 months

Case2: Outstanding transferred to a new card

As done in the previous case, we need to convert the annual interest rate to a monthly interest rate and then calculate the number of months required to repay the loan. The calculation is shown below:

Particulars		Calculator	Comments
Yearly Interest Rate	8.20%
Monthly Interest Rate	0.68%	I/Y	Converted to monthly
Monthly Payment	250	PMT	Payment made
Loan Outstanding	12000	PV	Card Balance Outstanding
Future Value	0.00	FV	Complete Repayment
Repayment Tenor	58.37	N	Months required to repay

Using Calculator: The notations have been given above. Enter the values in the scond column in the notations given in third column and calculate 'N" accordingly.

Using Excel: Use the NPER formula as: = NPER (0.68%, 250, -12000, 0 ,0)

Hence, on the new card, the loan can be repaid in approximately 59 months

Answer: The loan can be repaid 30 months earlier on the new card as compared to the old one. (89 months - 59 months)

Case3: 2% Fee charged on balance transferred

Here, with the 2% fee chargs on the transgerring of balance, the loan outstanding would increase. i.e.

Amount to be repaid = Balance Transferred * (1 + 2%)

Amount to be repaid = 12000 * 1.02 = $ 12,240

Now, the same calculation needs to be done as done in Case2.

Particulars		Calculator	Comments
Yearly Interest Rate	8.20%
Monthly Interest Rate	0.68%	I/Y	Converted to monthly
Monthly Payment	250	PMT	Payment made
Loan Outstanding	12240	PV	Card Balance Transferred
Future Value	0.00	FV	Complete Repayment
Repayment Tenor	59.81	N	Months required to repay

If 2% charges are levied, 60 months would be required to repay the outstanding balance.

Hence, if 2% charges are levied on transfer of outstanding balance, then the balance can still be repaid 29 months earlier on the new card as compared to the old one. (89 months - 60 months)