INTEREST TABLES AND THEIR CONTENTS . FUTURE VALUE OF 1 TABLE. Contains the amoun

Question

INTEREST TABLES AND THEIR CONTENTS . FUTURE VALUE OF 1 TABLE. Contains the amounts to which 1 will accumulate if deposited now at a specified rate and left for a specified number of periods (Table 6.1). Table 6.1 FUTURE VALUE OF 1 (FUTURE VALUE OF A SINGLE SUM) (a)Periods 2% 29,% 3% 02000 1.02500 103000 104000 10000 1.06000 2 1.04040 105063 106090 108160 110250 112360 3106121 1.07689 109273 1.1248615763 119102 08243 1038 112551 116986 12155 126248 L10408 1.13141 115927 121665 127628 133823 12616115969 1.19405 126532 134010 141852 7L14869 1.18869 122987 131593140710 150363 17166 121840 126677 136857 147746 1.59385 L19509 1.24886 130477 142331 55133 168948 21899 128008 134392 148024 162889 1.79085 124337 131209 138423 153945 1.71034 1.89830 1.26824 134489 142576 160103 1.79586 201220 129361 13785 146853 66507 188565 2.13293 31948 141297 15129 1.73168 1.97993 226090 15 134587 144830 1557971.800942.07893 239656 37279 148451 16047 187298 2.18287 2 54035 140024 152162 1652SS 194790 229202 2.69277 42825 13966 1.70243 20258 24066 285434 1.45681 159865 1.75351 210685 2.52695 302560 148595 163862 1806 2.19112 265330 3.20714 51567 167958 186029 227877 2.78596 3.39956 154598 1.72157 191610 236992 2.92526 30354 1 57690 7646 197359 246472 3.07152 3.81975 24 160844 180873 20329 256330 3.22510 40489 12 13 14 17 18 19 21 64061 185394 209378 2.66584 3.38635 429187 26 167342 1.90029 215659 2.77247 3.55567 454938 1.70689 194780 222129 288337 3.73346 4.82235 174102 199650 228793 299870 3.92013 5.11169 177584 204641 235657 3,11865 4.11614 541839 27 28

Explanation / Answer

Answer a Present value of option a = $55,220 Answer b Using present value of annuity formula , we can calculate the present value. Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = ? P = amount payable at the end of each quarter = $4050 r = rate of interest per quarter = 2.50% n = no.of quarters = 5 years * 4 = 20 Present value of annuity = 4050 x {[1 - (1+0.0250)^-20]/0.0250} Present value of annuity = 4050 x 15.58916 Present value of option b = $63,136 Answer c Using present value of annuity due formula , we can calculate the present value of $1961 quarterly payments Present value of annuity due = P + P x {[1 - (1+r)^-(n-1)]/r} Present Value of annuity due = ? P = Quarterly payment = $1961 r = rate of interest per quarter = 2.50% n = no.of quarters = 10 years * 4 = 40 Present value of annuity due = 1961 + 1961 x {[1 - (1+0.025)^-(40-1)]/0.025} Present value of annuity due = 1961 + 1961 x 24.73034 Present value of quarterly payments = $50,457 Present value of option c = $19,610 + $50,457 = $70,067 Answer d Using present value of annuity formula , we can calculate the present value of $4050 quarterly payments Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = ? P = amount payable at the end of each quarter = $4050 r = rate of interest per quarter = 2.50% n = no.of quarters = 3 years * 4 = 12 Present value of annuity = 4050 x {[1 - (1+0.025)^-12]/0.025} Present value of annuity = 4050 x 10.25776 = 41544 Present value of $4050 quarterly payments = $41,544 Using present value of annuity formula , we can calculate the present value of $1460 quarterly payments at the end of 3 rd year Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = ? P = amount payable at the end of each quarter = $1460 r = rate of interest per quarter = 2.50% n = no.of quarters = 25 Present value of annuity = 1460 x {[1 - (1+0.025)^-25]/0.025} Present value of annuity = 1460 x 18.42438 = 26900 Present value of $1460 quarterly payments = $26900 * [1/1.025^3] Present value of $1460 quarterly payments = $24,979 Present value of Option d = $41,544 + $24,979 = $66,523 The final answer Alan should exercise Option c as this option has highest present value.

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