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1  The sale of a house calls for  payments of P950 at the end of each month for 25 years,if money is worth 18%, m= 12 what single payment today is equally acceptable?

2   A commercial bank pays interest at 13%, m= 2 on all the time deposits,what sequence of equal deposits at the end each six months for 5 years would accumulate for p120,000?

3    To provide for his daughter”s college educations, a man deposits P2,000 at the end of each 3 month for 6 years ,if the money draws 9%  interest converted quarterly , how much does the fund contain after 6 years?

4    A couple left an inheritance to thier 7 years old son an amount of p6,000 a year, the money was deposited in a bank which offers 8% , m=1 , if the first payment was made on the child’s 10th birthday  and the last payment on his 21st birthday ,, what amount will the child receive after the last payment?

Question 1

In this particular question, the payment at the end of each month is $ 950 for a period which needs to be discounted considering a discount rate of 18/12 = 1.5% per month as shown in the table below.

Month

Payment Made ($)

Present Value ($)

1

950

935.96

2

950

922.13

3

950

908.50

4

950

895.08

5

950

881.85

6

950

868.82

7

950

855.98

8

950

843.33

9

950

830.86

10

950

818.58

11

950

806.49

12

950

794.57

13

950

782.83

14

950

771.26

15

950

759.86

16

950

748.63

17

950

737.57

18

950

726.67

19

950

715.93

20

950

705.35

21

950

694.92

22

950

684.65

23

950

674.54

24

950

664.57

25

950

654.75

26

950

645.07

27

950

635.54

28

950

626.14

29

950

616.89

30

950

607.77

31

950

598.79

32

950

589.94

33

950

581.22

34

950

572.64

35

950

564.17

36

950

555.84

37

950

547.62

38

950

539.53

39

950

531.55

40

950

523.70

41

950

515.96

42

950

508.33

43

950

500.82

44

950

493.42

45

950

486.13

46

950

478.95

47

950

471.87

48

950

464.89

49

950

458.02

50

950

451.25

51

950

444.59

52

950

438.02

53

950

431.54

54

950

425.16

55

950

418.88

56

950

412.69

57

950

406.59

58

950

400.58

59

950

394.66

60

950

388.83

61

950

383.08

62

950

377.42

63

950

371.85

64

950

366.35

65

950

360.94

66

950

355.60

67

950

350.35

68

950

345.17

69

950

340.07

70

950

335.04

71

950

330.09

72

950

325.21

73

950

320.41

74

950

315.67

75

950

311.01

76

950

306.41

77

950

301.88

78

950

297.42

79

950

293.03

80

950

288.70

81

950

284.43

82

950

280.23

83

950

276.08

84

950

272.00

85

950

267.98

86

950

264.02

87

950

260.12

88

950

256.28

89

950

252.49

90

950

248.76

91

950

245.08

92

950

241.46

93

950

237.89

94

950

234.38

95

950

230.91

96

950

227.50

97

950

224.14

98

950

220.83

99

950

217.56

100

950

214.35

101

950

211.18

102

950

208.06

103

950

204.98

104

950

201.96

105

950

198.97

106

950

196.03

107

950

193.13

108

950

190.28

109

950

187.47

110

950

184.70

111

950

181.97

112

950

179.28

113

950

176.63

114

950

174.02

115

950

171.45

116

950

168.91

117

950

166.42

118

950

163.96

119

950

161.53

120

950

159.15

121

950

156.80

122

950

154.48

123

950

152.20

124

950

149.95

125

950

147.73

126

950

145.55

127

950

143.40

128

950

141.28

129

950

139.19

130

950

137.13

131

950

135.11

132

950

133.11

133

950

131.14

134

950

129.20

135

950

127.29

136

950

125.41

137

950

123.56

138

950

121.73

139

950

119.93

140

950

118.16

141

950

116.42

142

950

114.70

143

950

113.00

144

950

111.33

145

950

109.69

146

950

108.06

147

950

106.47

148

950

104.89

149

950

103.34

150

950

101.82

151

950

100.31

152

950

98.83

153

950

97.37

154

950

95.93

155

950

94.51

156

950

93.12

157

950

91.74

158

950

90.38

159

950

89.05

160

950

87.73

161

950

86.44

162

950

85.16

163

950

83.90

164

950

82.66

165

950

81.44

166

950

80.23

167

950

79.05

168

950

77.88

169

950

76.73

170

950

75.60

171

950

74.48

172

950

73.38

173

950

72.29

174

950

71.22

175

950

70.17

176

950

69.14

177

950

68.11

178

950

67.11

179

950

66.12

180

950

65.14

181

950

64.18

182

950

63.23

183

950

62.29

184

950

61.37

185

950

60.47

186

950

59.57

187

950

58.69

188

950

57.82

189

950

56.97

190

950

56.13

191

950

55.30

192

950

54.48

193

950

53.68

194

950

52.88

195

950

52.10

196

950

51.33

197

950

50.57

198

950

49.82

199

950

49.09

200

950

48.36

201

950

47.65

202

950

46.94

203

950

46.25

204

950

45.57

205

950

44.89

206

950

44.23

207

950

43.58

208

950

42.93

209

950

42.30

210

950

41.67

211

950

41.06

212

950

40.45

213

950

39.85

214

950

39.26

215

950

38.68

216

950

38.11

217

950

37.55

218

950

36.99

219

950

36.45

220

950

35.91

221

950

35.38

222

950

34.85

223

950

34.34

224

950

33.83

225

950

33.33

226

950

32.84

227

950

32.35

228

950

31.88

229

950

31.41

230

950

30.94

231

950

30.48

232

950

30.03

233

950

29.59

234

950

29.15

235

950

28.72

236

950

28.30

237

950

27.88

238

950

27.47

239

950

27.06

240

950

26.66

241

950

26.27

242

950

25.88

243

950

25.50

244

950

25.12

245

950

24.75

246

950

24.38

247

950

24.02

248

950

23.67

249

950

23.32

250

950

22.97

251

950

22.63

252

950

22.30

253

950

21.97

254

950

21.64

255

950

21.32

256

950

21.01

257

950

20.70

258

950

20.39

259

950

20.09

260

950

19.79

261

950

19.50

262

950

19.21

263

950

18.93

264

950

18.65

265

950

18.37

266

950

18.10

267

950

17.84

268

950

17.57

269

950

17.31

270

950

17.06

271

950

16.80

272

950

16.56

273

950

16.31

274

950

16.07

275

950

15.83

276

950

15.60

277

950

15.37

278

950

15.14

279

950

14.92

280

950

14.70

281

950

14.48

282

950

14.27

283

950

14.06

284

950

13.85

285

950

13.64

286

950

13.44

287

950

13.24

288

950

13.05

289

950

12.85

290

950

12.66

291

950

12.48

292

950

12.29

293

950

12.11

294

950

11.93

295

950

11.76

296

950

11.58

297

950

11.41

298

950

11.24

299

950

11.08

300

950

10.91

Total

 

62,605.86

Hence the equivalent payment which can be made today is $ 62,606 approximately.

Question 2

Rate of interest = 13% pa or 6.5% for six months

Here we need to find the FV factor for the various payments which are made of 6 months.

Half Year

Payment Made

Future Value

1

1

1.76

2

1

1.65

3

1

1.55

4

1

1.46

5

1

1.37

6

1

1.29

7

1

1.21

8

1

1.13

9

1

1.07

10

1

1.00

Total

 

13.4944

Let the equal payments made at the end of 6 months be $x

Then 13.4944 x = 120000

Hence x = $8,892.6 which can be rounded off to $8,893

Question 3

Money deposited after every 3 months = $ 2,000

Time period for which this is continued = 6 years

Interest rate = 9% pa = 2.25% per quarter

Hence the value of  the fund at the end of the six years can be estimated as shown below.

Quarter

Payment Made

Future Value

1

2000

3336.46

2

2000

3263.04

3

2000

3191.24

4

2000

3121.02

5

2000

3052.34

6

2000

2985.17

7

2000

2919.49

8

2000

2855.24

9

2000

2792.41

10

2000

2730.97

11

2000

2670.87

12

2000

2612.10

13

2000

2554.62

14

2000

2498.41

15

2000

2443.43

16

2000

2389.66

17

2000

2337.08

18

2000

2285.65

19

2000

2235.36

20

2000

2186.17

21

2000

2138.06

22

2000

2091.01

23

2000

2045.00

24

2000

2000.00

Total

 

62,734.81

Hence the estimated value of the fund at the end of six years would be $ 62,735 approximately.

Question 4

Money received each year = $ 6,000

Applicable interest rate = 8% annually

The amount due at the 21st birthday is calculated as shown below.

Birthday

Payment made

Value at 21st birthday

10

6000

13,989.83

11

6000

12,953.55

12

6000

11,994.03

13

6000

11,105.58

14

6000

10,282.95

15

6000

9,521.25

16

6000

8,815.97

17

6000

8,162.93

18

6000

7,558.27

19

6000

6,998.40

20

6000

6,480.00

21

6000

6,000.00

Total

 

113,862.76

Hence the amount received at 21st birthday by the child would be $113,863 approximately.