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