Question

T owe $25,000 on a credit card at 27.9% effective. If I pay $600 at the end of every month, how much will I owe after 3 years? [3 marks]

Answer 1

Balance owed after 3 years = $23,961.77

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The balance of the loan after 3 years can be found by constructing the amortization schedule of the loan

The monthly interest is found by using the following formula

Interest = ( 27.9% $\div$ 12 ) $\times$ Beginning balance

For example, in the first month, interest = ( 0.279/12) $\times$ $ 25,000 = $ 581.25

Principal paid in 1st month = Monthly payment - interest = $ 600 - $ 581.25 = $ 18.75

Balance at end of 1st month = Beginning balance - principal paid

Balance at end of 1st month = $ 25,000 - $ 18.75 = $ 24,981.25

The beginning balance for the second month will be the ending balance of the first month.

The same technique is applied to calculate the interest paid, principal paid and ending balance.

The table can be developed using excel. The formulas used is shown as below:-

Month	Beginning balance	Monthly payment	Interest	Principal	Ending balance
1	25000	600	=(0.279/12)*B2	=C2-D2	=B2-E2
=A2+1	=F2	600	=(0.279/12)*B3	=C3-D3	=B3-E3
=A3+1	=F3	600	=(0.279/12)*B4	=C4-D4	=B4-E4
=A4+1	=F4	600	=(0.279/12)*B5	=C5-D5	=B5-E5
=A5+1	=F5	600	=(0.279/12)*B6	=C6-D6	=B6-E6
=A6+1	=F6	600	=(0.279/12)*B7	=C7-D7	=B7-E7
=A7+1	=F7	600	=(0.279/12)*B8	=C8-D8	=B8-E8
=A8+1	=F8	600	=(0.279/12)*B9	=C9-D9	=B9-E9
=A9+1	=F9	600	=(0.279/12)*B10	=C10-D10	=B10-E10
=A10+1	=F10	600	=(0.279/12)*B11	=C11-D11	=B11-E11
=A11+1	=F11	600	=(0.279/12)*B12	=C12-D12	=B12-E12
=A12+1	=F12	600	=(0.279/12)*B13	=C13-D13	=B13-E13
=A13+1	=F13	600	=(0.279/12)*B14	=C14-D14	=B14-E14
=A14+1	=F14	600	=(0.279/12)*B15	=C15-D15	=B15-E15
=A15+1	=F15	600	=(0.279/12)*B16	=C16-D16	=B16-E16
=A16+1	=F16	600	=(0.279/12)*B17	=C17-D17	=B17-E17
=A17+1	=F17	600	=(0.279/12)*B18	=C18-D18	=B18-E18
=A18+1	=F18	600	=(0.279/12)*B19	=C19-D19	=B19-E19
=A19+1	=F19	600	=(0.279/12)*B20	=C20-D20	=B20-E20
=A20+1	=F20	600	=(0.279/12)*B21	=C21-D21	=B21-E21
=A21+1	=F21	600	=(0.279/12)*B22	=C22-D22	=B22-E22
=A22+1	=F22	600	=(0.279/12)*B23	=C23-D23	=B23-E23
=A23+1	=F23	600	=(0.279/12)*B24	=C24-D24	=B24-E24
=A24+1	=F24	600	=(0.279/12)*B25	=C25-D25	=B25-E25
=A25+1	=F25	600	=(0.279/12)*B26	=C26-D26	=B26-E26
=A26+1	=F26	600	=(0.279/12)*B27	=C27-D27	=B27-E27
=A27+1	=F27	600	=(0.279/12)*B28	=C28-D28	=B28-E28
=A28+1	=F28	600	=(0.279/12)*B29	=C29-D29	=B29-E29
=A29+1	=F29	600	=(0.279/12)*B30	=C30-D30	=B30-E30
=A30+1	=F30	600	=(0.279/12)*B31	=C31-D31	=B31-E31
=A31+1	=F31	600	=(0.279/12)*B32	=C32-D32	=B32-E32
=A32+1	=F32	600	=(0.279/12)*B33	=C33-D33	=B33-E33
=A33+1	=F33	600	=(0.279/12)*B34	=C34-D34	=B34-E34
=A34+1	=F34	600	=(0.279/12)*B35	=C35-D35	=B35-E35
=A35+1	=F35	600	=(0.279/12)*B36	=C36-D36	=B36-E36
=A36+1	=F36	600	=(0.279/12)*B37	=C37-D37	=B37-E37

Month	Beginning balance	Monthly payment	Interest paid	Principal paid	Ending balance
1	$25,000	$600	$581.25	$18.75	$24,981.25
2	$24,981.25	$600	$580.81	$19.19	$24,962.06
3	$24,962.06	$600	$580.37	$19.63	$24,942.43
4	$24,942.43	$600	$579.91	$20.09	$24,922.34
5	$24,922.34	$600	$579.44	$20.56	$24,901.79
6	$24,901.79	$600	$578.97	$21.03	$24,880.75
7	$24,880.75	$600	$578.48	$21.52	$24,859.23
8	$24,859.23	$600	$577.98	$22.02	$24,837.21
9	$24,837.21	$600	$577.47	$22.53	$24,814.67
10	$24,814.67	$600	$576.94	$23.06	$24,791.62
11	$24,791.62	$600	$576.41	$23.59	$24,768.02
12	$24,768.02	$600	$575.86	$24.14	$24,743.88
13	$24,743.88	$600	$575.30	$24.70	$24,719.17
14	$24,719.17	$600	$574.72	$25.28	$24,693.89
15	$24,693.89	$600	$574.13	$25.87	$24,668.03
16	$24,668.03	$600	$573.53	$26.47	$24,641.56
17	$24,641.56	$600	$572.92	$27.08	$24,614.47
18	$24,614.47	$600	$572.29	$27.71	$24,586.76
19	$24,586.76	$600	$571.64	$28.36	$24,558.40
20	$24,558.40	$600	$570.98	$29.02	$24,529.39
21	$24,529.39	$600	$570.31	$29.69	$24,499.69
22	$24,499.69	$600	$569.62	$30.38	$24,469.31
23	$24,469.31	$600	$568.91	$31.09	$24,438.22
24	$24,438.22	$600	$568.19	$31.81	$24,406.41
25	$24,406.41	$600	$567.45	$32.55	$24,373.86
26	$24,373.86	$600	$566.69	$33.31	$24,340.55
27	$24,340.55	$600	$565.92	$34.08	$24,306.47
28	$24,306.47	$600	$565.13	$34.87	$24,271.60
29	$24,271.60	$600	$564.31	$35.69	$24,235.91
30	$24,235.91	$600	$563.48	$36.52	$24,199.40
31	$24,199.40	$600	$562.64	$37.36	$24,162.03
32	$24,162.03	$600	$561.77	$38.23	$24,123.80
33	$24,123.80	$600	$560.88	$39.12	$24,084.68
34	$24,084.68	$600	$559.97	$40.03	$24,044.65
35	$24,044.65	$600	$559.04	$40.96	$24,003.68
36	$24,003.68	$600	$558.09	$41.91	$23,961.77