Assume that you have a balance of $3200 on your MasterCard and that you make no...

Assume that you have a balance of $3200 on your MasterCard and that you make no more charges. Assume that MasterCard charges 12% APR and that each month you make only the minimum payment of 6% of the balance.

What will the balance be after 24 months? (Round your answer to the nearest cent.)

Expert Solution

Given details in the question,

APR, or the interest rate yearly is 12% p.a.
Hence, the monthly rate is 12%/12, or r = 1% every month
The balance outsatnding at the start of the term is $3200.

Payment of 6% of the balance amount is made only every month.
Hence, to solve and find out the final value outstanding after 24 months, we need to apply the applicable monthly interest rate on the outstanding amount and add the Interest Amount to the outstanding value, pay off 6% off of it, and then use the same remaining and oustanding balance for computing the balance for next month. The calculation for the same is shown in the form of a table below.

TimeLine	Outstanding Amount (Principal at Beginning of Month)	Total Amount due (Principal * (1+r))	Net Outstanding Balance for next month (Total Amount Due - 6% Payment Made) or (0.94* Total Amount Due)
Month 1	3200	3232	3038.08
Month 2	3038.08	3068.4608	2884.353152
Month 3	2884.353152	2913.196684	2738.404883
Month 4	2738.404883	2765.788931	2599.841595
Month 5	2599.841595	2625.840011	2468.289611
Month 6	2468.289611	2492.972507	2343.394156
Month 7	2343.394156	2366.828098	2224.818412
Month 8	2224.818412	2247.066596	2112.2426
Month 9	2112.2426	2133.365026	2005.363125
Month 10	2005.363125	2025.416756	1903.891751
Month 11	1903.891751	1922.930668	1807.554828
Month 12	1807.554828	1825.630376	1716.092554
Month 13	1716.092554	1733.253479	1629.258271
Month 14	1629.258271	1645.550853	1546.817802
Month 15	1546.817802	1562.28598	1468.548821
Month 16	1468.548821	1483.23431	1394.240251
Month 17	1394.240251	1408.182654	1323.691694
Month 18	1323.691694	1336.928611	1256.712895
Month 19	1256.712895	1269.280024	1193.123222
Month 20	1193.123222	1205.054454	1132.751187
Month 21	1132.751187	1144.078699	1075.433977
Month 22	1075.433977	1086.188317	1021.017018
Month 23	1021.017018	1031.227188	969.3535567
Month 24	969.3535567	979.0470922	920.3042667

Hence, we can see from the table that at the end of 24 months, the net balance left to be paid rounded off to the nearest cent is $920.30

jeff jeffy answered 1 year ago

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