Elmazi-Shkumbin-Week2-2A

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New Jersey Institute Of Technology *

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492

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Industrial Engineering

Date

Oct 30, 2023

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docx

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Shkumbin Elmazi Professor Tchouassi IE 492 9/15/23 2A Assigned Questions-Schaums Chapters 1-2 Our goal is to have $1,000,000 in 20 years in an investment account that is available to withdraw starting 21st year. To that end, we are evaluating multiple options and will pick the most preferred option and why. For this problem, we assume that we have required cash on hand at the present time for investment. Option #1: Put aside lump sum today, at 8% interest compounded annually. i = 8% n = 20 F = $1,000,000 P = F * (F/P,i%,n)-1 = $1,000,000 * (F/P,8%,20)-1 = $1,000,000 * (4.6610)-1 =214,546.23 Invest $214,546.23 today as lump sum to have $1,000,000 in 20 years at 8% interest compounded annually. Option #2: Invest a specific amount over time (over the next 18 years) at 10% compounded annually. A =? i = 10% n = 18 F = $1,000,000 A=F * (A/F,i%,n) = F * (F/A,i%,n)^-1 = $1,000,000 * (F/A,10%,18)^-1 = $1,000,000 *(45.5992)^-1 =21930.2093 21,930.21 x 18 = $394,743.78 Invest, $394,743.78 today to have $1,000,000 at the end of 20 years based on investment strategy of option 2. Option #3: Put aside a lump sum today, at 8% interest compounded annually for 10 years, at which point the account balance in the 10th year reinvests in another account over next 10 years (specific amount for this account is withdrawn and reinvested in another account every year) at 10% interest compounded annually. The first account stops earning interest at the end of 10th year. A = F * (A/F,i%,n) = F * (F/A,i%,n)^-1 = $1,000,000 * (F/A,8%,10)^-1 = $1,000,000 *(14.4866)^-1 =69029.30984 10 * $69,029.30 = $690,293.1 P = F * (F/P,i%,n)^-1 = $690,293.1 * (F/P,10%,10)^-1 = $690,293.1, * (2.5937)^-1 =266142.2292 Therefore, you need to invest $266,142.23 today to have $1,000,000 at the end of 20 years based on investment strategy of option 3.

Conclusion In conclusion, option 1 the investment is $214,546.23, option 2 the investment is $394,743.78, and option 3 the investment is $266,142.23. Clearly option 1 is the preferred method because it requires the least amount of investment to reach one million dollars.

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