Use Worksheet 11.1. Alison Conroy is early in her career and is now employed as
ID: 2802082 • Letter: U
Question
Use Worksheet 11.1. Alison Conroy is early in her career and is now employed as the managing editor of a well-known business journal. Although she thoroughly enjoys her job and the people she works with, she would really like to be a literary agent. She would like to go on her own in about five years and figures she'll need about $ 75,000 in capital to do so. Given that she thinks she can make about 12 percent on her money, use Worksheet 11.1 to answer the following questions. How much would Alison have to invest today, in one lump sum, to end up with $ 75,000 in five years? Round the answer to two decimal places. $ If she's starting from scratch, how much would she have to put away annually to accumulate the needed capital in five years? Round the answer to two decimal places. $ How about if she already has $ 5,000 socked away; how much would she have to put away annually to accumulate the required capital in five years? Round the answer to two decimal places. DETERMINING AMOUNT OF INVESTMENT CAPITAL Financial goal: 1. Targeted Financial Goal (see Note 1) $ 2. Projected Average Return on Investments % A. Finding a Lump Sum Investment: 3. Future Value Factor, from Appendix A • based on years to target date and a projected average return on investment of % 1.000 4. Required Lump Sum Investment • line 1 ÷ line 3 $- B. Making a Series of Investments over Time: 5. Amount of Initial Investment, if any (see Note 2) $ 6. Future Value Factor, from Appendix A • based on years of target date and a projected average return on investment of % 1.000 7. Terminal Value of Initial Investment • line 5 × line 6 $- 8. Balance to Come from Savings Plan • line 1 - line 7 $- 9. Future Value Annuity Factor, from Appendix B • based on years to target date and a projected average return on investment of % 0.00 10. Series of Annual Investments Required over Time • line 8 ÷ line 9 $- Note 1: "The “targeted financial goal” is the amount of money you want to accumulate by some target date in the future." Note 2: "If you’re starting from scratch—i.e., there is no initial investment—enter zero on line 5, skip lines 6 and 7, and then use the total targeted financial goal (from line 1) as the amount to be funded from a savings plan; now proceed with the rest of the worksheet."
Explanation / Answer
ASSUMPTION: Alison requires the $75000 at the end of Year 5. (So that the money is actually compounded for 5 whole years and the lumpsum is available to Alison only at the end of Year 5)
(1) Let lumpsum to be deposited at current date be $ K.
% Return on Money = 12%
Future Value of $ K is $ 75000
Therefore, by Time Value of Money = K x (1+(12/100))^(5) =75000 (A)
Solving equation (A) we get K = $ 42557.01
(2) Let Alison save equal amount of $K every year for five years so as to end up with accumulated savings of $75000 at the end of the fifth year.This is a stream of equal cash flows every year starting from end of Year 0 (now) and going upto end of Year 4. The total future value of all these equal annual cash flows compounded at 12% should be equal to the final value of $75000.
Future Value of first deposit at end of Year 0 = K x (1+(12/100))^(5)
Future Value of second deposit at end of Year 1 = K x (1+(12/100))^(4)
Future Value of third deposit at end of Year 2 = K x (1+(12/100))^(3)
Future Value of fourth deposit at end of Year 3 = K x (1+(12/100))^(2)
Future Value of fifth deposit at end of Year 4 = K x (1+(12/100))^(1)
Summing, all the future value equations given above, equating it to $75000 and solving the resultant equation would give the value of equal annual savings required.
K x (1+(12/100))^(5) + K x (1+(12/100))^(4) + K x (1+(12/100))^(3) + K x (1+(12/100))^(2) + K x (1+(12/100))^(1) =75000
Therefore, K = $ 10540.83
(3) If Alison already has $ 5000 with her then the future value of this initial amount at 12 % annual interest would be (1+(12/100))^(5) x 5000 = $8811.71
Therefore, amount to be accumulated through annual savings = Required Amount - Future Value of Initial Money = 75000 - 8811.71 = $ 66188.29
The sum of the future value of equal annual savings beginning from end of Year 0 and going upto end of Year 4 should be equal to the remaining amount of $ 66188.29
Therefore, K x (1+(12/100))^(5) + K x (1+(12/100))^(4) + K x (1+(12/100))^(3) + K x (1+(12/100))^(2) + K x (1+(12/100))^(1) = 66188.29
Solving the above equation we get , K = $ 9302.39
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