Q no 13 ( ordinary annuity )
The Happy Hang Glide Company is purchasing a building and gas obtained a $190000 mortgage loan for 20 years. This loan bears a compound annual interest rate of 17 % and calls for equal annual installments payments at the end of each of the 20 year. What is the amount of the annual payment?
Solution:
P.V = $ 190000
No. of years = 20
Rate of interest = 17 %
We know that
P.V of annuity = P[ 1-(1+r)-n/r]
P = $33760
Q no 14: (Amortization)
Establish loan amortization schedule for the following loans to the nearest cent if a 36 month loan of $8000 with equal instalments payments at the end of each months. The interest rate is 1 % per month?
Solution:
No. of months = 36
P.V = $8000
r = 1 % per month
P.V of annuity = P[1-(1+r)-n/r]
P.V = $ 265.71
Months
|
Instalments
|
Interest
|
Principal
|
Balance
|
0
|
-
|
-
|
-
|
8000
|
1
|
265.7101
|
80
|
185.7101
|
7814.29
|
2
|
265.7101
|
78.1429
|
187.5672
|
7626.723
|
3
|
265.7101
|
76.26723
|
189.4429
|
7437.28
|
4
|
265.7101
|
74.3728
|
191.3373
|
7245.943
|
5
|
265.7101
|
72.45943
|
193.2507
|
7052.692
|
6
|
265.7101
|
70.52692
|
195.1832
|
6857.509
|
7
|
265.7101
|
68.57509
|
197.135
|
6660.374
|
8
|
265.7101
|
66.60374
|
199.1064
|
6461.267
|
9
|
265.7101
|
64.61267
|
201.0974
|
6260.17
|
10
|
265.7101
|
62.6017
|
203.1084
|
6057.061
|
11
|
265.7101
|
60.57061
|
205.1395
|
5851.922
|
12
|
265.7101
|
58.51922
|
207.1909
|
5644.731
|
13
|
265.7101
|
56.44731
|
209.2628
|
5435.468
|
14
|
265.7101
|
54.35468
|
211.3554
|
5224.113
|
15
|
265.7101
|
52.24113
|
213.469
|
5010.644
|
16
|
265.7101
|
50.10644
|
215.6037
|
4795.04
|
17
|
265.7101
|
47.9504
|
217.7597
|
4577.281
|
18
|
265.7101
|
45.77281
|
219.9373
|
4357.343
|
19
|
265.7101
|
43.57343
|
222.1367
|
4135.207
|
20
|
265.7101
|
41.35207
|
224.358
|
3910.849
|
21
|
265.7101
|
39.10849
|
226.6016
|
3684.247
|
22
|
265.7101
|
36.84247
|
228.8676
|
3455.379
|
23
|
265.7101
|
34.55379
|
231.1563
|
3224.223
|
24
|
265.7101
|
32.24223
|
233.4679
|
2990.755
|
25
|
265.7101
|
29.90755
|
235.8025
|
2754.953
|
26
|
265.7101
|
27.54953
|
238.1606
|
2516.792
|
27
|
265.7101
|
25.16792
|
240.5422
|
2276.25
|
28
|
265.7101
|
22.7625
|
242.9476
|
2033.302
|
29
|
265.7101
|
20.33302
|
245.3771
|
1787.925
|
30
|
265.7101
|
17.87925
|
247.8308
|
1540.094
|
31
|
265.7101
|
15.40094
|
250.3092
|
1289.785
|
32
|
265.7101
|
12.89785
|
252.8122
|
1036.973
|
33
|
265.7101
|
10.36973
|
255.3404
|
781.6325
|
34
|
265.7101
|
7.816325
|
257.8938
|
523.7388
|
35
|
265.7101
|
5.237388
|
260.4727
|
263.2661
|
36
|
265.7101
|
2.632661
|
263.0774
|
0.188612
|
Q no. 15:
You have borrowed $ 14300 at a compound annual interest rate of 15%. You feel that you will be able to make annual payments of $3000 per year on your loan. (Payments include both principal and interest.)How long will it be before the loan is entirely paid off(to the nearest year)?
Solution:
P.V = $14300
Rate of interest = 15%
Payments = $3000
P.V of annuity = P[1-(1+r)-n/r]
14300 = 3000[1-(1+0.15)-n/0.15]
n = 9 years
Q no. 16:
Lost Dutchman Mines, inc., is considering investing in Peru. It makes a bid to the government to participate in the development of a mine, the profit of which will be realized at the end of five years. The mine is expected to produce $ 500000 in cash to Lost Dutchman Mines at that time. Other than the bid at the outset, no other cash flows will occur, as the government will reimburse the company for all costs. If Lost Dutchman requires a nominal annual return of 20 %(ignoring any tax consequences) , what is the maximum bid it should make for the participation right of interest is compounded(a) annually ?(b) semi annually?(c)countinuously?
Solution:
(a)
F.V = $500000
r = 20% p.a
n = 5 years
P.V = ?
P.V = F.V (1+r)-n
P.V = 500000(1+0.20)-5
P.V = $200938
(b) semi annually
P.V = F.V(1+r/m)-n*m100
P.V =500000(1+0.20/2)-5*2
P.V = $192771
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