In: Finance
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.)
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