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

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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