Dixon Shuttleworth has a large sum of money that he wants to invest to finance h

Question

Dixon Shuttleworth has a large sum of money that he wants to invest to finance his retirement. He has been presented with three options. The first investment offers a 5% return for the first five years, a 10% return for the next five years, and a 20% return thereafter. The second investment offers 10% for the first ten years and 15% thereafter. The third investment offers a constant 12% rate of return. Determine which of these investments is the best for Dixon if he plans to retire in the following number of years. A. Fifteen years B. Twenty years C. Thirty years

Explanation / Answer

Lets assume that $100 is to be Invested A. 15 yrs Op1: 1st 5 yr 5%, next 5yr 10% & then next 5Yr 20% Future value FV at Y5 = PV*(1+r)^n = 100*(1+5%)^5 = 128 FV at Y10 = 128*(1+10%)^5 = 206 FV at Y15 = 206*(1+20%)^5 = 513 SO In Option 1, He will get 5.13 times in 15 Yrs Op II : 1st 10 yr 10%, next 5yr 15% Future value FV at Y10 = PV*(1+r)^n = 100*(1+10%)^10 = 259 FV at Y15 = 259*(1+15%)^5 =521 SO In Option 2, He will get 5.21 times in 15 Yrs Op III: 12% Future value FV at Y15 = PV*(1+r)^n = 100*(1+12%)^15 =547 SO In Option 3, He will get 5.47 times in 15 Yrs So for A: 15 Yrs, Option III is Best .............................Ans (A) B. 20 yrs Op1: 1st 5 yr 5%, next 5yr 10% & then next 10Yr 20% Future value FV at Y5 = PV*(1+r)^n = 100*(1+5%)^5 = 128 FV at Y10 = 128*(1+10%)^5 = 206 FV at Y20 = 206*(1+20%)^10 =1275 SO In Option 1, He will get 12.75 times in 20 Yrs Op II : 1st 10 yr 10%, next 10yr 15% Future value FV at Y10 = PV*(1+r)^n = 100*(1+10%)^10 = 259 FV at Y20 = 259*(1+15%)^10 = 1048 SO In Option 2, He will get 10.48 times in 20Yrs Op III: 12% Future value FV at Y20 = PV*(1+r)^n = 100*(1+12%)^20 =965 SO In Option 3, He will get 9.65 times in 20 Yrs So for B: 20 Yrs, Option I is Best ........................................Ans (B) C. 30 yrs Op1: 1st 5 yr 5%, next 5yr 10% & then next 20Yr 20% Future value FV at Y5 = PV*(1+r)^n = 100*(1+5%)^5 = 128 FV at Y10 = 128*(1+10%)^5 = 206 FV at Y30 = 206*(1+20%)^20 =7898 SO In Option 1, He will get 78.98 times in 30 Yrs Op II : 1st 10 yr 10%, next 20yr 15% Future value FV at Y10 = PV*(1+r)^n = 100*(1+10%)^10 = 259 FV at Y30 = 259*(1+15%)^20 = 4239 SO In Option 2, He will get 42.39 times in 30 Yrs Op III: 12% Future value FV at Y20 = PV*(1+r)^n = 100*(1+12%)^30 = 2996 SO In Option 3, He will get 29.96 times in 30 Yrs So for C: 30 Yrs, Option I is Best ........................................Ans (C)

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