A young couple planning ahead for their retire­ment has decided that $3 million is the amount they will need in order to retire comfortably 20 years from now. For the past 5 years, they have been able to invest one of their salaries ($50,000 per year, which includes employer contributions) while living off the other salary. They plan to start a family sometime in the next 10 years and when they will have their first child, one of the parents will quit working, causing the savings to decrease to $10,000 per year thereafter. If they have realized an average ROR of 10% per year on their invest­ments, and expect to continue at this ROR, is reaching their goal of $3 million in 20 years sensi­tive to when they have their first child (i.e., be­tween now and 10 years from now)? If so, how

Question

many years from now will they have to wait before they have their first child? Use a future worth analysis.

What will be an ideal response?

Answer 1

Start family now: FW = 50,000(F/A,10%,5)(F/P,10%,20) + 10,000(F/A,10%,20)
= 50,000(6.1051)(6.7275) + 10,000(57.2750)
= $2,626,353 (< $3,000,000)

Child 1 year from now: FW = 50,000(F/A,10%,6)(F/P,10%,19) + 10,000(F/A,10%,19)
= 50,000(7.7156)(6.1159) + 10,000(51.1591)
= $2,870,953 (< $3,000,000)

Child 2 years from now: FW = 50,000(F/A,10%,7)(F/P,10%,18) + 10,000(F/A,10%,18)
= 50,000(9.4872)(5.5599) + 10,000(45.5992)
= $3,093,386 (> $3,000,000)

Their retirement goal is sensitive to when they start a family; wait 2 (or more) years