Question

Your money is tied up and you need to borrow $10,000. The following two alternatives are available at different banks:

(1) Pay $3,311.61 at the end of each year for 5 years, starting at the end of the first year (5 payments total at 18 percent nominal per year compounded monthly which equates to 19.56 percent effective); or
(2) pay $253.93 at the end of each month for 5 years, starting at the end of the first month (60 payments total at 18 percent nominal per year compounded monthly).

Which will result in the smaller PW of payments to you if:

1) your TVOM is 16 percent nominal per year compounded monthly?

1a) PW, Alternative 1: $

1b) PW, Alternative 2: $

2) your TVOM is 21 percent nominal per year compounded monthly?

2a) PW, Alternative 1: $

2b) PW, Alternative 2: $

Answer 1

Total repayment in alternative 1 = $3311.61 x 5 = $16558.05

Total repayment in alternative 2 = $253.93 x 60 = $15235.80

It can be seen that the total repayment in alternative 2 is less than the total repayment in alternative 1 hence, alternative 2 should be selected. This is due to monthly repayments of principal amount makes the yearly interest payment lesser.

Present worth = Cash flow / ((1 + interest rate) ^ number of periods)

Net Present Worth = Sum of the present worth of all the cash flows

Below table values have been calculated by the above formulae

Year	Cashflow	Interest	PW	NPW
1	$3,311.61	16%	$2,854.84	$10,843.18
2	$3,311.61	16%	$2,461.07
3	$3,311.61	16%	$2,121.61
4	$3,311.61	16%	$1,828.97
5	$3,311.61	16%	$1,576.70

Month	Cashflow	Interest	PW	NPW
1	$253.93	1.33%	$250.59	$10,442.03
2	$253.93	1.33%	$247.29
3	$253.93	1.33%	$244.04
4	$253.93	1.33%	$240.83
5	$253.93	1.33%	$237.66
6	$253.93	1.33%	$234.53
7	$253.93	1.33%	$231.44
8	$253.93	1.33%	$228.40
9	$253.93	1.33%	$225.39
10	$253.93	1.33%	$222.43
11	$253.93	1.33%	$219.50
12	$253.93	1.33%	$216.61
13	$253.93	1.33%	$213.76
14	$253.93	1.33%	$210.95
15	$253.93	1.33%	$208.18
16	$253.93	1.33%	$205.44
17	$253.93	1.33%	$202.73
18	$253.93	1.33%	$200.07
19	$253.93	1.33%	$197.43
20	$253.93	1.33%	$194.84
21	$253.93	1.33%	$192.27
22	$253.93	1.33%	$189.74
23	$253.93	1.33%	$187.25
24	$253.93	1.33%	$184.78
25	$253.93	1.33%	$182.35
26	$253.93	1.33%	$179.95
27	$253.93	1.33%	$177.58
28	$253.93	1.33%	$175.25
29	$253.93	1.33%	$172.94
30	$253.93	1.33%	$170.66
31	$253.93	1.33%	$168.42
32	$253.93	1.33%	$166.20
33	$253.93	1.33%	$164.02
34	$253.93	1.33%	$161.86
35	$253.93	1.33%	$159.73
36	$253.93	1.33%	$157.63
37	$253.93	1.33%	$155.55
38	$253.93	1.33%	$153.51
39	$253.93	1.33%	$151.49
40	$253.93	1.33%	$149.49
41	$253.93	1.33%	$147.53
42	$253.93	1.33%	$145.58
43	$253.93	1.33%	$143.67
44	$253.93	1.33%	$141.78
45	$253.93	1.33%	$139.91
46	$253.93	1.33%	$138.07
47	$253.93	1.33%	$136.26
48	$253.93	1.33%	$134.46
49	$253.93	1.33%	$132.69
50	$253.93	1.33%	$130.95
51	$253.93	1.33%	$129.22
52	$253.93	1.33%	$127.52
53	$253.93	1.33%	$125.85
54	$253.93	1.33%	$124.19
55	$253.93	1.33%	$122.56
56	$253.93	1.33%	$120.94
57	$253.93	1.33%	$119.35
58	$253.93	1.33%	$117.78
59	$253.93	1.33%	$116.23
60	$253.93	1.33%	$114.70

Year	Cashflow	Interest	PW	NPW
1	$3,311.61	21%	$2,736.87	$9,689.72
2	$3,311.61	21%	$2,261.87
3	$3,311.61	21%	$1,869.32
4	$3,311.61	21%	$1,544.89
5	$3,311.61	21%	$1,276.77

Month	Cashflow	Interest	PW	NPW
1	$253.93	1.75%	$249.56	$9,386.26
2	$253.93	1.75%	$245.27
3	$253.93	1.75%	$241.05
4	$253.93	1.75%	$236.91
5	$253.93	1.75%	$232.83
6	$253.93	1.75%	$228.83
7	$253.93	1.75%	$224.89
8	$253.93	1.75%	$221.02
9	$253.93	1.75%	$217.22
10	$253.93	1.75%	$213.49
11	$253.93	1.75%	$209.81
12	$253.93	1.75%	$206.21
13	$253.93	1.75%	$202.66
14	$253.93	1.75%	$199.17
15	$253.93	1.75%	$195.75
16	$253.93	1.75%	$192.38
17	$253.93	1.75%	$189.07
18	$253.93	1.75%	$185.82
19	$253.93	1.75%	$182.62
20	$253.93	1.75%	$179.48
21	$253.93	1.75%	$176.40
22	$253.93	1.75%	$173.36
23	$253.93	1.75%	$170.38
24	$253.93	1.75%	$167.45
25	$253.93	1.75%	$164.57
26	$253.93	1.75%	$161.74
27	$253.93	1.75%	$158.96
28	$253.93	1.75%	$156.22
29	$253.93	1.75%	$153.54
30	$253.93	1.75%	$150.90
31	$253.93	1.75%	$148.30
32	$253.93	1.75%	$145.75
33	$253.93	1.75%	$143.24
34	$253.93	1.75%	$140.78
35	$253.93	1.75%	$138.36
36	$253.93	1.75%	$135.98
37	$253.93	1.75%	$133.64
38	$253.93	1.75%	$131.34
39	$253.93	1.75%	$129.08
40	$253.93	1.75%	$126.86
41	$253.93	1.75%	$124.68
42	$253.93	1.75%	$122.54
43	$253.93	1.75%	$120.43
44	$253.93	1.75%	$118.36
45	$253.93	1.75%	$116.32
46	$253.93	1.75%	$114.32
47	$253.93	1.75%	$112.36
48	$253.93	1.75%	$110.42
49	$253.93	1.75%	$108.52
50	$253.93	1.75%	$106.66
51	$253.93	1.75%	$104.82
52	$253.93	1.75%	$103.02
53	$253.93	1.75%	$101.25
54	$253.93	1.75%	$99.51
55	$253.93	1.75%	$97.80
56	$253.93	1.75%	$96.11
57	$253.93	1.75%	$94.46
58	$253.93	1.75%	$92.84
59	$253.93	1.75%	$91.24
60	$253.93	1.75%	$89.67