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Retirement planning: Capital depletion model

Please help arrive at the capital depletion model for a couple.

If a married couple is each 43.
Husband makes 75000
Wife makes 50000
Required Rate of REturn is 8%
Inflation rate is 3%

If they retire at 62 what is the total needed assuming 80% wage replacement ratio to age 96? My calculations are below. Are they correct?
PV - 100,000 (80% of 125,000)
N-19
i - 3
FV 175,350

Find Lump sum that they need to have to get to age 96 (beg mode)
PMT - 175,350
N 34 (96-62)
i [(1.08/1.03)-1]x100
PVAD 3,390,948

How much do they need to save? Below is portfolio

STock Portfolio = 200,000
401K = 250,000 (adding 7,500 annually)
IRA = 28,000

PV = 478,000
i = 8
n = 19
FV 2,062,905

Needed 3,390,948
FV of Lump 2,062,905
Difference is 1,328,043

What is additional that needs to be saved?
FV = 1,328,043
n=228 (19x12)
i.0067 (8% / 12)
PMT 5,780

Are these numbers correct?
What do we do to figure Social Security changing how much is needed to save....Head of House - 29,996; Spouse - 22,468, beginning at age 62, 65, 67?
At age 62 they will have reduced benefits of 75.8% of SS
At age 65 they will have 94.4%
At age 67 they will have 100%.

Solution Summary

The solution provides a capital depletion model for retirement planning for a married couple.

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