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Question: future value of an ordinary annuity of 1 is...

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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 + IR

    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.)

 

 

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