Question

"The maker of a solar power system is offering it for sale with an attractive finance loan that involves low payments over a five year period and then a lump sum payment at the end of the five years. The solar power system costs $13,500 and buyers of the system will pay regular monthly instalments for 59 months and then in month 60 payout the loan with a payment of $3,500. If the loan rate is 8.4%p.a. what is the amount of the regular monthly payment?"

169.49

207.48

280.1

231.58

232.31

Answer 1

• All working forms part of the answer
• The amount of monthly 59 payments will be equal to the Amount to repaid ‘divided by’ the present value of annuity for 59^th term.
• Annuity is the sum of present values, the calculation is given below:

No. of payments	PV $1 at 8.4% [0.7% monthly]
1	0.993048659
2	0.98614564
3	0.979290606
4	0.972483223
5	0.965723161
6	0.95901009
7	0.952343685
8	0.945723619
9	0.939149572
10	0.932621224
11	0.926138256
12	0.919700353
13	0.913307203
14	0.906958494
15	0.900653916
16	0.894393164
17	0.888175932
18	0.882001919
19	0.875870823
20	0.869782347
21	0.863736193
22	0.857732069
23	0.851769681
24	0.84584874
25	0.839968957
26	0.834130047
27	0.828331725
28	0.822573709
29	0.816855719
30	0.811177477
31	0.805538706
32	0.799939132
33	0.794378482
34	0.788856487
35	0.783372877
36	0.777927385
37	0.772519747
38	0.767149699
39	0.76181698
40	0.756521331
41	0.751262493
42	0.746040212
43	0.740854232
44	0.735704302
45	0.730590171
46	0.72551159
47	0.720468312
48	0.715460091
49	0.710486684
50	0.705547849
51	0.700643346
52	0.695772935
53	0.690936381
54	0.686133446
55	0.681363899
56	0.676627507
57	0.671924038
58	0.667253266
59	0.662614961
TOTAL	48.19786274

• The same can also be calculated by MS-Excel function as “=pmt(0.084/12,59,10000,0)”
• Total loan = $ 13,500, amount repayable in 60^th month = $ 3,500.

Amount repayable in 59 months = 13500 – 3500 = $ 10,000

• Monthly amount = $ 10,000 / 48.19786274 [calculated above]

= $ 207.48

• Correct answer = Option #2 - $ 207.48