Question

If I made a £400 credit card purchase at the start of the month and make the minimum payment on the last day of each month, investigate the effect of payment over 6 months.

Card has an APR of 19% and a minimum payment % of 3%

Answer 1

Effect of above transactions for 6 month can be tabled as below.

Month	Initial Principal	Interest for the month	total due at end of month	Paid of due @3%	Balance carry forward for next month
1	400.00	6.28	406.28	12.19	394.09
2	394.09	6.19	400.28	12.01	388.27
3	388.27	6.10	394.37	11.83	382.54
4	382.54	6.01	388.55	11.66	376.89
5	376.89	5.92	382.81	11.48	371.33
6	371.33	5.83	377.16	11.31	365.85

So at end of 6 month the due amount will be 365.85 and total payment is 70.48 out of which interest payment is 36.33

Working

Calculation of interest for daily compounding basis for first month on initial principal amount

P (1 + r/n)^nt - P

P = principal

r= rate

n = No of days in year

t = days for which interest is to be calculated i.e. 30/365 here for all condition

= P (1 + 19/(100 x 365))^365 x 30/365 -P

= P (1 + 19/36500) ^ 30 -P

= P (1 + 0.00052) -P

= P (1.0157) -P

So for 1st Month = 400 x 1.0157 -400 = 6.28

2 month = 394.09 x 1.0157 - 394.09 = 6.19

3 Month = 388..27 x 1.0157 - 388.27 = 6.10

4 MOnth = 382.54 x 1.0157 - 382.54 = 6.01

5 Month = 376.89 x 1.0157 - 376.89 = 5.92

6 Month = 371.33 x 1.0157 - 371.33 = 5.83

So this is the solution.