The expenses associated with sending two children through college prevented Vict

Question

The expenses associated with sending two children through college prevented Victor and Maria Hernandez from adding substantially to their investment program. Now that their younger son, Joseph, has completed school and is working full time, they would like to build up their investments quickly. Victor is 47 years old and wants to retire early, perhaps by age 60. In addition to the retirement program at his place of employment, Victor believes that their investment portfolio, currently valued at $120,000, will need to triple to $360,000 by his planned retirement time, in 13 years. He and Maria realize that they will have to sacrifice a lot of current spending to save and invest for retirement.

(a) What rate of return is needed on the $120,000 portfolio to reach their goal of $360,000 (assuming no additional contributions)? Use Appendix A-1

Explanation / Answer

FV = PV X FVIF@ R%, 13 YEARS

360000 = 120000 X FVIF @R%, 13 YEARS

3 = FVIF @R%, 13 YEARS

R is between 8% & 9%

FVIF @8% FOR 13 YEARS = 2,7196

FVIF @9% FOR 13 YEARS = 3.0658

BY USING INTERPOLATION, WE CAN FIND EXACT RATE:

FORMULA = LOWER RATE + (FVIF REQUIRED - FVIF @8%)/(FVIF @ 9% - FVIF @ 8%)

FORMULA = 8 + (3 - 2.7196)/(3.0658 -2.7196) = 8.8104% = 8.81% ANSWER

ANY DOUBTS, FEEL FREE TO ASK

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