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[SOLVED] 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

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

Expert Answer

 

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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