- Math
- Mathematics
- future value of an ordinary annuity of 1 is...
Question: future value of an ordinary annuity of 1 is...
Question details
Future value of an ordinary annuity of $1 ( is the number of time periods)
|
Table of future value interest factors |
||||||||||
|
interest rate per period |
||||||||||
|
period n |
1% |
2% |
3% |
4% |
5% |
6% |
7% |
8% |
9% |
10% |
|
1 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
1.0000 |
|
2 |
2.0100 |
2.0200 |
2.0300 |
2.0400 |
2.0500 |
2.0600 |
2.0700 |
2.0800 |
2.0900 |
2.1000 |
|
3 |
3.0301 |
3.0604 |
3.0909 |
3.1216 |
3.1525 |
3.1836 |
3.2149 |
3.2464 |
3.2781 |
3.3100 |
|
4 |
4.0604 |
4.1216 |
4.1836 |
4.2465 |
4.3101 |
4.3746 |
4.4399 |
4.5061 |
4.5731 |
4.6410 |
|
5 |
5.1010 |
5.2040 |
5.3091 |
5.4163 |
5.5256 |
5.6371 |
5.7507 |
5.8666 |
5.9847 |
6.1051 |
|
6 |
6.1520 |
6.3081 |
6.4684 |
6.6330 |
6.8019 |
6.9753 |
7.1533 |
7.3359 |
7.5233 |
7.7156 |
|
7 |
7.2135 |
7.4343 |
7.6625 |
7.8983 |
8.1420 |
8.3938 |
8.6540 |
8.9228 |
9.2004 |
9.4872 |
|
8 |
8.2857 |
8.5830 |
8.8923 |
9.2142 |
9.5491 |
9.8975 |
10.2598 |
10.6366 |
11.0285 |
11.4359 |
|
9 |
9.3685 |
9.7546 |
10.1591 |
10.5828 |
11.0266 |
11.4913 |
11.9780 |
12.4876 |
13.0210 |
13.5795 |
|
10 |
10.4622 |
10.9497 |
11.4639 |
12.0061 |
12.5779 |
13.1808 |
13.8164 |
14.4866 |
15.1929 |
15.9374 |
|
11 |
11.5668 |
12.1687 |
12.8078 |
13.4864 |
14.2068 |
14.9716 |
15.7836 |
16.6455 |
17.5603 |
18.5312 |
|
12 |
12.6825 |
13.4121 |
14.1920 |
15.0258 |
15.9171 |
16.8699 |
17.8885 |
18.9771 |
20.1407 |
21.3843 |
|
13 |
13.8093 |
14.6803 |
15.6178 |
16.6268 |
17.7130 |
18.8821 |
20.1406 |
21.4953 |
22.9534 |
24.5227 |
|
14 |
14.9474 |
15.9739 |
17.0863 |
18.2919 |
19.5986 |
21.0151 |
22.5505 |
24.2149 |
26.0192 |
27.9750 |
|
15 |
16.0969 |
17.2934 |
18.5989 |
20.0236 |
21.5786 |
23.2760 |
25.1290 |
27.1521 |
29.3609 |
31.7725 |
|
16 |
17.2579 |
18.6393 |
20.1569 |
21.8245 |
23.6575 |
25.6725 |
27.8881 |
30.3243 |
33.0034 |
35.9497 |
|
17 |
18.4304 |
20.0121 |
21.7616 |
23.6975 |
25.8404 |
28.2129 |
30.8402 |
33.7502 |
36.9737 |
40.5447 |
|
18 |
19.6147 |
21.4123 |
23.4144 |
25.6454 |
28.1324 |
30.9057 |
33.9990 |
37.4502 |
41.3013 |
45.5992 |
|
19 |
20.8109 |
22.8406 |
25.1169 |
27.6712 |
30.5390 |
33.7600 |
37.3790 |
41.4463 |
46.0185 |
51.1591 |
|
20 |
22.0190 |
24.2974 |
26.8704 |
29.7781 |
33.0660 |
36.7856 |
40.9955 |
45.7620 |
51.1601 |
57.2750 |
|
21 |
23.2392 |
25.7833 |
28.6765 |
31.9692 |
35.7193 |
39.9927 |
44.8652 |
50.4229 |
56.7645 |
64.0025 |
|
22 |
24.4716 |
27.2990 |
30.5368 |
34.2480 |
38.5052 |
43.3923 |
49.0057 |
55.4568 |
62.8733 |
71.4027 |
|
23 |
25.7163 |
28.8450 |
32.4529 |
36.6179 |
41.4305 |
46.9958 |
53.4361 |
60.8933 |
69.5319 |
79.5430 |
|
24 |
26.9735 |
30.4219 |
34.4265 |
39.0826 |
44.5020 |
50.8156 |
58.1767 |
66.7648 |
76.7898 |
88.4973 |
|
25 |
28.2432 |
32.0303 |
36.4593 |
41.6459 |
47.7271 |
54.8645 |
63.2490 |
73.1059 |
84.7009 |
98.3471 |
|
26 |
29.5256 |
33.6709 |
38.5530 |
44.3117 |
51.1135 |
59.1564 |
68.6765 |
79.9544 |
93.3240 |
109.1818 |
|
27 |
30.8209 |
35.3443 |
40.7096 |
47.0842 |
54.6691 |
63.7058 |
74.4838 |
87.3508 |
102.7231 |
121.0999 |
|
28 |
32.1291 |
37.0512 |
42.9309 |
49.9676 |
58.4026 |
68.5281 |
80.6977 |
95.3388 |
112.9682 |
134.2099 |
|
29 |
33.4504 |
38.7922 |
45.2189 |
52.9663 |
62.3227 |
73.6398 |
87.3465 |
103.9659 |
124.1354 |
148.6309 |
|
30 |
34.7849 |
40.5681 |
47.5754 |
56.0849 |
66.4388 |
79.0582 |
94.4608 |
113.2832 |
136.3075 |
164.4940 |
|
31 |
36.1327 |
42.3794 |
50.0027 |
59.3283 |
70.7608 |
84.8017 |
102.0730 |
123.3459 |
149.5752 |
181.9434 |
|
32 |
37.4941 |
44.2270 |
52.5028 |
62.7015 |
75.2988 |
90.8898 |
110.2182 |
134.2135 |
164.0370 |
201.1378 |
|
33 |
38.8690 |
46.1116 |
55.0778 |
66.2095 |
80.0638 |
97.3432 |
118.9334 |
145.9506 |
179.8003 |
222.2515 |
|
34 |
40.2577 |
48.0338 |
57.7302 |
69.8579 |
85.0670 |
104.1838 |
128.2588 |
158.6267 |
196.9823 |
245.4767 |
|
35 |
41.6603 |
49.9945 |
60.4621 |
73.6522 |
90.3203 |
111.4348 |
138.2369 |
172.3168 |
215.7108 |
271.0244 |
|
36 |
43.0769 |
51.9944 |
63.2759 |
77.5983 |
95.8363 |
119.1209 |
148.9135 |
187.1021 |
236.1247 |
299.1268 |
|
37 |
44.5076 |
54.0343 |
66.1742 |
81.7022 |
101.6281 |
127.2681 |
160.3374 |
203.0703 |
258.3759 |
330.0395 |
|
38 |
45.9527 |
56.1149 |
69.1594 |
85.9703 |
107.7095 |
135.9042 |
172.5610 |
220.3159 |
282.6298 |
364.0434 |
|
39 |
47.4123 |
58.2372 |
72.2342 |
90.4091 |
114.0950 |
145.0585 |
185.6403 |
238.9412 |
309.0665 |
401.4478 |
|
40 |
48.8864 |
60.4020 |
75.4013 |
95.0255 |
120.7998 |
154.7620 |
199.6351 |
259.0565 |
337.8824 |
442.5926 |
Section A: Loans and Annuities
1. Mr and Mrs Tweed borrow $450 000 to buy a house. The loan is at 9% p.a. reducible interest and the monthly repayment is $3775.50.
a) Copy and complete the table showing the progress of Mr and Mrs Tweed’s loan for the first 3 months.
|
Month |
Principal (P) |
Interest (I) |
P + I |
P + I |
|
1 |
$450 000 |
$3375 |
|
|
|
2 |
|
|
|
|
|
3 |
|
|
|
|
b) After three months, how much have Mr and Mrs Tweed paid off the principal of their loan?
For the following question use the table attached at the end of this assignment.
2. Hamish invests $3000 at the end of every quarter for the next 7 years into an account with interest calculated at 8% p.a. compounded quarterly.
a) Convert the interest rate of 8% p.a. to an interest rate per quarter.
b) How many quarters are there in 7 years?
c) Use the table at the end of the assignment to find the future value of this annuity at the end of 7 years.
3. Yousef has a credit card that has no annual fees and charges a flat rate of 19.75% p.a. interest on all purchases. If interest is charged from the day of purchase, what is the interest charged on purchases totalling $3125 for 28 days? (Answer to the nearest cent.)
Solution by an expert tutor
