Question

Jim recently received a credit card with a 15% nominal interest rate. With the card, he purchased a new computer for $2,000.00. The minimum monthly payment on the card is $70 per month. If he makes the minimum monthly payment and makes no other charges, how many months will it take him to pay off the card?

		28.57 months
		35.57 months
		50.25 months
		67.20 months
		70.57 months

Answer 1

The initial Principal is $2,000 and the monthly payments of $70 go towards monthly interest and principal. We can calculate interest amount for 1st month which is $2,000 *15%/12 = $25. Remaining $ 45 will adjust against the principal and outstanding will reduce to $1,955. We repeat the process of subsequent months and after 35 months the remaining principal is $39.31 which will become $39.8 including the interest for the month. So, the total repayment time is 35 + (39.8/70) = 35.57 months. A detailed calculation is given below.

Monthly payments	Interest	Principal	$ 2,000.00
70	$    25.00	$    45.00	$ 1,955.00
70	$    24.44	$    45.56	$ 1,909.44
70	$    23.87	$    46.13	$ 1,863.31
70	$    23.29	$    46.71	$ 1,816.60
70	$    22.71	$    47.29	$ 1,769.30
70	$    22.12	$    47.88	$ 1,721.42
70	$    21.52	$    48.48	$ 1,672.94
70	$    20.91	$    49.09	$ 1,623.85
70	$    20.30	$    49.70	$ 1,574.15
70	$    19.68	$    50.32	$ 1,523.83
70	$    19.05	$    50.95	$ 1,472.87
70	$    18.41	$    51.59	$ 1,421.28
70	$    17.77	$    52.23	$ 1,369.05
70	$    17.11	$    52.89	$ 1,316.16
70	$    16.45	$    53.55	$ 1,262.61
70	$    15.78	$    54.22	$ 1,208.40
70	$    15.10	$    54.90	$ 1,153.50
70	$    14.42	$    55.58	$ 1,097.92
70	$    13.72	$    56.28	$ 1,041.65
70	$    13.02	$    56.98	$     984.67
70	$    12.31	$    57.69	$     926.97
70	$    11.59	$    58.41	$     868.56
70	$    10.86	$    59.14	$     809.42
70	$    10.12	$    59.88	$     749.54
70	$       9.37	$    60.63	$     688.91
70	$       8.61	$    61.39	$     627.52
70	$       7.84	$    62.16	$     565.36
70	$       7.07	$    62.93	$     502.43
70	$       6.28	$    63.72	$     438.71
70	$       5.48	$    64.52	$     374.19
70	$       4.68	$    65.32	$     308.87
70	$       3.86	$    66.14	$     242.73
70	$       3.03	$    66.97	$     175.76
70	$       2.20	$    67.80	$     107.96
70	$       1.35	$    68.65	$        39.31