Please help me with this one ! The expenses of sending two children through coll

Question

Please help me with this one !

The expenses of sending two children through college prevented Victor and Maria Hernandez from adding substantially to their investment program. Now that their younger son John has completed school and is working full-time, however, 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 present investment portfolio valued at $70,000 will need to triple to $210,000 by retirement time.

A- What rate of return is needed on the $70,000 portfolio to reach the goal of $210,000?Use the Appendix A.3

B. Victor and Maria think they will need a total of $400,000 for a retirement nest egg. Therefore, they will need to create an additional sum of $190,000 through new investments. Assuming an annual return of 8 percent , how much do the Hernandezes need to invest each year to reach the goal of $190,000? Use Appendix A.3

C- If they assume only an 6 percent annual return, how much do the Hernandezes need to invest each year to reach the goal of $190,000?

Thanks !

Explanation / Answer

A) The PV is $70000 and the FV is $210000 after 13 years (60-47)

So 210000 = 70000*FVIF(i,13)

3 = FVIF(i,13)

from the FVIF tables the factor of 3 falls between i = 9% and 8%

8% = 2.7196

9% = 3.0658

So exact rate = 9 - 0.0658/(3.0658-2.7196) = 8.81%

B) The goal of $190000 is the future value of the annuity.

So 190000 = A*fvifa(8,13)

190000 = A*21.4953

A = $8,839.14

C) If the interest rate is 6%, then the equation becomes 190000 = A*fvifa(6,13)

A = 190000/18.8821 = $10,062.44

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