1. After starting to turn significant profit, Lumyn Electronics decided that an
ID: 2884568 • Letter: 1
Question
1. After starting to turn significant profit, Lumyn Electronics decided that an investment account for their future expansion plans is now necessary. The company's goal is to expand to a major mall location for which $100,000 would be needed. If the investment account pays 12% interest compounded monthly, what would their initial investment have to be in order to reach their $100,000 goal in 5 years?
2. Lumyn Electronics is now using social networking to expand their reputation and reach new potential customers. The company has found that the number N of new potential customers in their 12,000 people community that have heard of their company can be modeled by the equation N = 12,000(1 - e-0.0008t) where t is the number of days elapsed since starting using social networking. How long will it take for 100 new potential customers to have heard of the company?
Explanation / Answer
1)
formula: A=P(1+(r/n))nt
A=100000,r=12%=0.12,t=5years ,n=12(compounded monthly)
=>100000=P(1+(0.12/12))12*5
=>100000=P(1.01)60
=>P=100000/(1.01)60
=>P=100000/1.816696698564090264988957004034
=>P=55044.961593775998060552392875111
initial investment have to be 55045 dollars
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2)
N=12000(1-e-0.0008t)
100 new potential customers =>N=100
=>12000(1-e-0.0008t)=100
=>(1-e-0.0008t)=100/12000
=>(1-e-0.0008t)=1/120
=>e-0.0008t=1-(1/120)
=>e-0.0008t=(119/120)
=>e0.0008t=(120/119)
=>0.0008t=ln(120/119)
=>t=(1/0.0008)ln(120/119)
=>t=10.46
it takes 10.46 days approximately
or it takes 11 days (as number of days are whole number)
PLEASE RATE IF HELPFUL.PLEASE COMMENT IF YOU HAVE ANY DOUBT
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