Question

Your parents have accumulated a $130,000 nest egg They have been planning to use this money to pay college costs to be incured by you and your sister, Courtney However, Courtney has decided to forgo college and start a nal salon. Your parents are giving Courtney $16.000 to hetp her get started, and they have decided to take year end vacancs costing $8.000 per year for the next four years Use 8 percent as the appropriate interest rate throughout this problem Use Appendix A and Appendix D for an approximate answer, but caculate your Snal answer using the formula and financial calculator methods a. How much money will your parents have at the end of four years to help you with graduate school, which you will start then? (Round your final answer to 2 decimal places.) Funds available for graduate school b. You plan to work on a master's and perhaps a PhD If graduate school costs $21.460 per year, approximatey how long will you be able to stay in school based on these funds? (Round your final answer to 2 decimal places.) Number of years N-P+ Appondis&a dS1,V Parcent 11% 10% 7 % 8 % 9% % 5% 4% 2% 2% 1% Paod 1.110 1.090 1.100 1,080 1070 1.000 1,050 100 1040 1010 1020 1.232 1210 1,188 1.166 1.124 1,145 1.100 102 1.125 1081 1040 1420 1.368 1295 1.331 1225 1260 1.158 1.191 1.09 100 1061 1.518 1.412 1.484 1311 1300 1216 1262 1.170 1.12 1082 1041 1686 1.539 1811 1408 1409 1278 1.338 1217 1.15 106 1.104 1870 1501 1.587 1677 1772 1,419 1285 1340 1.126 1.194 1062 1228 1.949 2076 1.504 150 1714 1316 1407 1.14 1230 1.0/2 1718 1851 1990 2.144 2305 1080 1369 1477 1.594 1.172 1,267 2.172 2.358 2.558 1423 156 1580 188 199 14 1.195 130 1480 1829 1.791 1.967 2159 2367 2.594 2839 105 1219 1344 1.116 1243 1808 2.105 233 2S80 2853 3.152 1384 1.530 1710 11 128 1.127 1425 1.801 179 2012 2.252 2.518 2813 3.138 3.498 1.665 1.138 1234 160 3.883 1886 2.133 2410 2720 3066 3452 14 1990 1se9 1319 1513 1.732 3.787 2261 2579 2837 3.342 4310 1,s61 134 2.39 2.50 1.508 1801 20/9 279 2.172 3542 4.177 4786 1.173 1.373 1805 1873 2183 2952 3426 3970 4595 5311 184 140 1.58 1.348 2232 2.093 a.159 3700 4.328 5.054 5800 196 1,42 1702 2.026 2407 2.854 4717 3330 3.996 5.560 6.544 1208 1457 1754 2.107 2597 3.026 3617 4316 5.142 6116 7.268 25 1220 14 1806 2191 2653 3870 3.207 4290 4.881 5504 727 8062 25 128 164 2064 256 3396 5427 6848 10 835 13 586 1348 1811 247 324 4222 5743 7812 10.06 13 258 31409 1/443 149 2208 322 4.01 040 19.296 14.9/4 21725 45259 00 155 2682 4.364 71 11467 18 420 29 457 46902 74 358 117 39 184 57 &osd Parcont Pariod 12% 12% 15 % s4% 16% 17% 18% 19% 20% 1 12 120 25% 114 1.150 30% 160 1170 1 100 125 1.180 2T1 1200 1250 1563 300 1.323 154 130 1 000 1369 1300 141 440 440 142 1521 156 1.802 1643 1874 1 1865 1728 2074 1749 1953 2441 181 1874 2197 100 2005 34 2011 200 2192 PREE 226 14 282 226e 2400 2 2313 2456 a252 3815 256 3/12 121 2700 262 2840 2 2.00 059 355 2 80 .00T 3001 265 33 4.021 4765 s.e 4/08 3511 10e 62/6 3759 435 121 4300 5160 5800 560 8157 0 66 75 4411 4807 5234 4228 12 617 5.624 9313 11842 6176 4 777 7430 17 s 25 206 728 8064 .596 11 42 1009 12 400 190 sse 10 147 22 77 119/4 10Te 1540 12 0 28422 at ee 1 14 M527 62 12an 4 6 T7m s244 22 1 2 2 221 2262 sec O Type here to search (1+0 PN,-A Prent value of an annuly of $1, P Apponds D Percent 8 % 12% 10% 11% 7% S% 6% 3% 4% 2% Perlod 0.901 9.893 0.909 0.935 0917 0.96 0952 0943 0.971 0.962 0.990 0.980 1.713 1.690 1.750 1.736 1783 1833 1808 1.913 1806 1.850 1.970 1.942 2 2.402 2444 2.531 2.487 2.577 2.775 2.723 2673 2.604 2.884 2 829 2941 3037 3170 3102 3312 3993 3240 3465 3367 3.902 3808 3717 3.630 3.546 3605 3.890 ומב 3696 4713 4452 4.329 4212 4.100 4 853 4580 4231 4486 4.355 4.111 5.076 4917 4767 4623 5206 5.795 6.728 5.601 5417 6.230 5242 5.033 4712 4.564 5.300 4868 6472 6.002 5786 5.582 5.335 5.146 4.968 5.971 5747 5.535 7.652 7.325 7.000 6733 6463 6210 5.537 5.328 5995 5.750 8.566 8162 7.786 7.435 7.108 6802 6515 6247 6.145 5889 5.650 9471 8983 8530 8111 7.722 7.360 7.004 6710 6418 5938 11 10.368 9787 9253 8760 8306 7.887 7499 7.139 6805 6.495 6207 12 11.255 10.575 9.954 9.385 7.536 7.161 6.814 6492 6.194 8863 8.384 7.943 13 12.134 11348 10635 7487 7.103 6.750 9.966 9.394 a853 8.358 7904 6.424 899 14 13004 12.106 11.296 10.563 11.938 6.982 28 9295 874 7.786 736 13.865 12.849 11.118 10.380 9.712 10.106 9108 8.559 8.061 7606 7.191 6811 16 13578 14718 10.838 1256 11.652 7 824 8.022 9447 8851 8313 7.379 6.974 171 15.562 13.166 14292 12.166 11.274 10.477 9.763 9.122 8.544 7.549 7.120 16.398 14.992 13.754 12.659 11.690 10826 10.059 9.372 8756 8201 7.702 7.250 17.226 15.678 14.324 12.085 12 462 13.134 11.158) 10.336 9.604 8950 365 7.839 7.366 20 18.046 16.351 14 877 13.590 11.470 10 594 9818 9.129 8514 7 469 7.963 22.023 25 15.622 18 523 17413 14094 12.783 11.654 10675 9.823 9.077 8422 7843 30 22.396 25.808 19.600 17.292 15.372 13.765 12 409 11.258 10274 8.055 9.427 8604 32 835 27.355 23.115 19793 17.159 15046 13.332 11.925 10.757 9.779 8.951 8244 50 18256 39.196 31 424 25.730 21.482 15762 13.801 12.233 10962 9915 9.042 8.304 Appondit D (cncluded Percent Period 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 35% 40% s0% 0.885 0877 0.870 0.862 0855 0847 0840 0833 0800 076 0741 0714 1 66 0 667 1.647 1626 1.605 1.585 1566 1547 152 440 1361 289 1224 2301 2.322 1311 2283 2246 2210 2174 2140 210 2639 952 2974 1.589 2914 407 285 2708 3274 2743 2 630 259 2362 214 3517 1997 3352 849 3430 1.605 3199 3127 3.058 2 6e9 29 2436 2220 3990 3809 2035 1732 3784 3686 3589 3496 3812 3410 3706 3326 3405 2951 3161 2643 2 802 4423 4.2 2385 2168 2 263 4160 824 MO 4.039 3 922 4799 2 508 4609 4482 4344 4202 4078 3.954 3 3309 s132 2825 2596 4 94 2331 4772 4.45 4.607 4300 4163 10 4.00 3463 3s7 5406 3019 0216 205 s019 2.39 4 833 940 4.0 4494 4339 4 430 5453 5224 2715 2752 279 245 2 5009 5197 2414 486 16 5918 3es6 560 317 3725 3 90 521 2438 1907 4790 542 6.000 s342 5406 1995 4310 A715 6302 4530 370 322 14 24 224 2400 2478 5.00 4611 614 2a14 004 626 54 32 5405 244 2 6729 40 s149 2834 222 6467 0 210 12 5000 0 244 soe 2 730 3

Answer 1

a)

amount available at beginning = 130000-16000 = 114,000

amount available after year 1 end = 114,000 * 1.08 = 123,120

amount available after year 2 beginning = 123,120 -8000 = 115,120

amount available after year 2 end = 115,120 * 1.08 = 124,329.60

amount available after year 3 beginning = 124,329.60 -8000 = 116,329.60

amount available after year 3 end = 116,329.60 * 1.08 = 125,635.97

amount available after year 4 beginning =125,635.97 -8000 =117,635.97

amount available after year 4 end = 117,635.97 * 1.08 =127,046.85

amount available after year 5 beginning = 127,046.85 -8000 = 119,046.85

money parents have at the end of four years = 119,046.85...........ans

b)

amount at the beginning = 119,046.85 - 21,460 = 97,586.85

amount at the beginning of next year = (97,586.85 * 1.08) - 21,460 =83,933.80

amount at the beginning of next year = (83,933.80 * 1.08) - 21,460 =69,188.50

amount at the beginning of next year = (69,188.50 * 1.08 ) - 21,460 = 53,263.58

amount at the beginning of next year = (53,263.58 * 1.08 ) - 21,460 = 36,064.67

amount at the beginning of next year = (36,064.67 * 1.08 ) - 21,460 = 17,489.84

amount at the beginning of next year = (17,489.84 * 1.08 ) - 21,460 = -2,570.97
hence

he will be able to stay for a period of seven  years 6 months in school

or u can do the question in this way also

Solution A
Year	Cash flow	Help for Salon	Vacation	Net Amount	FV factor @ 8%	Future value
0	130,000	(16,000)	-	114,000	1.3605	155,096
1			(8,000)	(8,000)	1.2597	(10,078)
2			(8,000)	(8,000)	1.1664	(9,331)
3			(8,000)	(8,000)	1.0800	(8,640)
4			(8,000)	(8,000)	1.0000	(8,000)
					Net Future value	119,047
So Parents will have 119,047 at the end of 4 years
Solution B
Annual Withdrawl	21460
So the PV of all such withdrawls should be equal to 119,047
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
119,047	=21460*(((1-(1 +8%) ^-n)) /8%)
119047/21460	=(((1-(1 +8%) ^-n)) /8%)
5.547	=(((1-(1 +8%) ^-n)) /8%)
=5.547*8%	=((1-(1 +8%) ^-n))
0.444	=((1-(1 +8%) ^-n))
=0.44376-1	=-(1 +8%) ^-n
(0.556)	=-(1 +8%) ^-n
0.556	=(1 +8%) ^-n
Log 0.556	=-nlog1.08
-0.2549	=-n*0.0334
=0.2549/0.0334	=n
n=	7.63
So he can survive in college for next 7.6 years