# (Question and Answer): Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your answer

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Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Present Value Years \$ 600 850 8,800 21,900 Interest Rate Future Value 8% \$ 1,393 2,330 367,247 382,983 12 18 14

 Solution: 1. Present Value Years Interest Rate Future Value \$600 10.94 8% \$1,393 850 8.90 12 2,330 18,800 17.96 18 367,247 21,900 21.84 14 382,983 Working Notes: Future value = Present Value (1+r)^t For \$600 10.94 8% \$1,393 Future value = Present Value (1+r)^t 1,393 = 600 (1+0.08)^t (1.08)^t = (1,393/600) taking log on both side (1.08)^t =2.32166 Log(1.08)^t = Log(2.32166) t x Log(1.08) = Log(2.32166) t=Log(2.32166)/Log(1.08) t= 0.3657986/0.0334237 t= 10.94 For 850 8.90 12 2,330 Future value = Present Value (1+r)^t 2,330 = 850(1+0.12)^t (1.12)^t = (2,330/850) taking log on both side (1.12)^t =2.741176 Log(1.12)^t = Log(2.741176) t x Log(1.12) = Log(2.741176) t=Log(2.741176)/Log(1.12) t= 0.4379369/0.0492180 t= 8.8979 t=8.90 For 18,800 17.96 18 367,247 Future value = Present Value (1+r)^t 367,247 = 18,800(1+0.18)^t (1.18)^t = (367,247/18,800) taking log on both side (1.18)^t =19.53441489 Log(1.18)^t = Log(19.53441489) t x Log(1.18) = Log(19.53441489) t=Log(19.53441489)/Log(1.18) t= 1.2908004074/0.071882007 t= 17.95721156 t=17.96 For 21,900 21.84 14 382,983 Future value = Present Value (1+r)^t 382,983 = 21,900(1+0.14)^t (1.14)^t = (382,983/21,900) taking log on both side (1.14)^t =17.48780822 Log(1.14)^t = Log(17.48780822) t x Log(1.14) = Log(17.48780822) t=Log(17.48780822)/Log(1.14) t= 1.2427353819/0.05690485 t= 21.83883064273 t=21.84 Notes: Exact value of t is calculation showing t value having more than two decimal , as per demand of question t value is round off to two decimal Log value is calculate from online calculator 2. Annual increase in selling price = 2.97% Working Notes Using formula Future value = Present Value (1+r)^t \$280,400=\$197,300(1+r)^12 (1+r)^12 = 280,400/197,300 (1+r)^12 = 1.421186011 (1+r) = (1.421186011)^(1/12) (1+r) = 1.029724178 r=1.029724178 – 1 r=0.029724178 r=2.97% Exact value of r is calculation showing r value having more than two decimal , as per demand of question r value is round off to two decimal

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