Question

A child receives 100,000 dollars as a gift which is deposited in a 6% bank account compounded semi-annually. If 5,000 dollars is withdrawn at the end of each half year, how long will the money last.

Answer 1

Given Principle : 100,000 Rede Interest rate= 6%. following iteration Compound (n)= Semi-Annually (2/yr) We will calculate this with We will use the following formule and to calculate amount et each at the end of every 6 month (7=0.5) nt A = Plito) R Principle A Amount se rate of interest modelo Semi - soumpounded ) t 0.5 (6 month) 0 Amount at the end of 6montha 103000 - 5000 = 198000 Amount at the end of 1 year 100g4o-5000=95940 Amount at the end of 1 year & 6 month 98818-5000 - 193818 @ Amount at the end of dyear 96632.5-50002 )976325 & Amount at the end of dyear &6 month 9438148-30 oo 89381.48 ③ Amount at the end of 3year 9 2062.92-5000:87062-92 6 Amount at the end of 3year & 6month 89674.81-5000= 184674.81 8 Amount at the end of 4y co 87215.05 - 2000- - 5000 = 182215.08 lor

2 syear (6) Amount at the end at the end of a year & 6 month 84 681,45-50002 79 681.45 1 Amount at the end of syear 82071.89.8000 = 770 71.89 1 Amount at the end of & 6month 79384.0-5000- 74384 2 Amont at the end of syear 76618.5-500 o- 71615.5 ① Amount at the end of byear & 6 month 73769.97-5000 = 6876]. 97 ① Amount at the end of 7 year 76826.89-5000 65826. 89. 15 Amount at the end of 7 year & 6 month 67801 70-5000 628017 16 Amount at the end of 8 year 64685.75-100059685. Ar Amount at the end of Byear & 6 month 8 61426.32-500o= 56476.32 18 Amount at the end of a year 58180.61 - 5000 53.170 61 Amount at the end of Iyear & Gmonth 54765.73-1000 = 49765.71 20 Amount at the end of 10 year (9) 51258.70-5000 46258.7 22 Amount at the end of loyeer & Gmonth 42646.46-50002 42646.46 13 Amount at the end of 11 year 43925.85-5000- 38925.85 22

3 6 Amount at the end of year & 6month 36146.44-10002 31146.44 12 400g3.69-5000 - 35099.63 Amount at the end of 12 year 2 Amount at the end of 12 year & month 32080-8.3-sodo=2208 0.83 Amount at the end of nyer B 27893-25-noos 22891.25 ( 28) Amount at the end of 13 year & month 23580.05-500 o=8 18580.65 2 Amount at the end of Myear 19137.45-500o= 14137.45 27) Amount at the end of 14 year & month 14561-57-5000= 9561157 E Amount at the end of 18 year 9898.42-5000= 4848.42 (29) Amount at the end of sy ear & 6 month 4993.87-000020 At the end of 15 year & 6month the amount will be ended Alternate Method "- logW - log (W-B1) logt log J. B2 1,00,000 J = 1.03 0 wasooo

h no log Good log (1:03) log (5000- looo oo X0-3 ) (103) log (1:0) N2 30.998 n = 11 months I'm in years = 15.5 years

Lola L D E F G Н. J к annual principal intrest half total withdraw (at end sr no principal rate yearly intrest principal n of year) 1 100000 0.06 0.03 3000 103000 5000 98000 2 98000 0.06 0.03 2940 100940 5000 95940 3 95940 0.06 0.03 2878.2 988182 5000 93818.2 4 93818.2 0.06 0.03 2814.546 96632.75 5000 91632.75 5 91632.75 0.06 0.03 2748.982 94381.73 5000 89381.73 6 89381.73 0.06 0.03 2681.452 92063.18 5000 87063.18 787063.18 0.06 0.03 2611.895 89675.08 5000 84675.08 884675.08 0.06 0.03 2540.252 87215.33 5000 82215.33 191 82215.63 0.06 0.03 2466.46 84681.79 5000 79681.79 1079681.79 0.06 0.03 2390.454 82072.24 5000 77072.24 + 177072.24 0.06 0.03 2312.167 79384.41 5000 74384.41 12 74884.41 0.06 0.03 2231.532 76615.94 5000 71615.94 137161594 0.06 0.03 2148.478 73764.42 5000 68764.42 14 68764.42 0.06 0.03 2062.933 70827 35 5000 65827.35 15 W 65827/35 0.06 0.03 1974.821 67802.17 5000 62802.17 16 62802017 0.06 0.03 1884.065 64686.24 5000 59686.24 1715968624 0.06 0.03 1790.587 61476.82 5000 56476.82 118 5647682 0.06 0.03 1694.305 58171.13 5000 53171.13 953171/13 0.06 0.03 1595.134 54766 26 5000 49766.26 20 49766 26 0.06 0.03 1492 988 51259.25 5000 46259.25 21 W46259 25 0.06 0.03 1387.778 47647 03 5000 42647 03 22 4264703 0.06 0.03 1279.411 43926.44 5000 38926.44 23 88926.44 0.06 0.03 1167.793 40094 23 5000 35094.23 24 W35094.23 0.06 0.03 1052 827 36147 06 5000 31147.06 25 31147.06 0.06 0.03 934 4118 32081.47 5000 27081.47 26 2708147 006 0.03 812.4441 27893.92 5000 22893.92 27 22893.92 0.06 0.06 686.8175 23580.73 5000 18580.73 28 18580 73 0.06 0.03 557 422 19138. 15 5000 14138 15 2914188.15 0.06 0 03 424 1446 14562.3 5000 95623 30 9562.3 0.06 0.03 286.869 9849.169 5000 4849 169 34849 169 0106 145 476 4994 644 6000 16165686 32 535626 0.06 OBLO 16069 -5.51705 5000 6005152 Cheet2 Sheet3 /