question archive Peter and Blair recently reviewed their future retirement income and expense projections
Peter and Blair recently reviewed their future retirement income and expense projections
Subject:FinancePrice:2.86 Bought7
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 15 years. They determined that they would have a retirement income of ?$77,000 in? today's dollars, but they would actually need ?$104,271 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income? shortfall, assuming a 3 percent inflation rate and a return of 8 percent. Click on the table icon to view the FVIF table LOADING...
. Click on the table icon to view the
.
The total amount that Peter and Blair must save if they wish to completely fund their income? shortfall, assuming a 3 percent inflation rate and a return of 8 percent is ?$
nothing
. ?(Round to the nearest? cent.)
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
This is a question of Present value of annuity and future value of annuity.
Inflation adjusted rate of return=[(1+rate of ret.)/(1+inflation)]-1
=(1.08/1.02)-1
=5.88%
They need additional income of $27271(i.e.104271-77000) per anum.
Hence they will need to invest the present value of annuity of $27271 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+.0588)^15-1] / [(1+.0588)^15*.0588)
=9.788855793
Present value of annuity=9.788855793*27271
=266951.8863
266951.8863 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+.0588)^25-1] / [.0588]
=53.94623434
Amount of annuity=266951.8863/53.94623434
=4948.480456
Hence they will have to invest$4948.480456 per annum for 25 years in order to earn extra $27271( each year for 15years after 25 years.
