Question

Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 25 years and anticipate they will need funding for an additional 13 years. They determined that they would have a retirement income of ​$45 comma 000 in​ today's dollars, but they would actually need ​$64 comma 417 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income​ shortfall, assuming a 2 percent inflation rate and a return of 11 percent.

Answer 1

This is a question of Present value of annuity and future value of annuity.

Inflatin adjusted rate of return=[(1+rate of ret.)/(1+inflation)]-1

=(1.11/1.02)-1

=.0882353 or 8.82353%

They need additional income of $19417(i.e.64417-45000) per anum.

Hence they will need to invest the present value of annuity of $19417 at 25th year end.

Present value of annuity=PV factor aof annuity*Annuity Amount

PV factor of annuity= [(1+r)^{^n}-1] / [(1+r)^{^n}*r]

=[(1+.0882353)^{^13}-1] / [(1+.0882353)^{^13}*.0882353]

=7.557949

Present value of annuity=7.557949*19417

=146752.7

146752.7 is the future value of annuity(i.e. annual saving) after 25th year.

Hence Amount of annuity shall be=Future value of annuity/FV Factor of annuity

FV factor of annuity=[(1+r)^{^n}-1] / [r]

=[(1+.0882353)^{^25}-1] / [.0882353]

=82.51528

Amount of annuity=146752.7/82.51528

=1778.49

Hence they will have to invest$1778.49 per anum for 25 years in order to earn extra 19417 each year for 13years after 25 years.

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