Suppose you are exactly 30 years old. You believe that you will be able to save for the next 20 years, until you are 50. For 10 years following that, and till your retirement at age 60, you will have a spike in your expenses due to your kids' college expenses, weddings, etc., and you will not be able to save. If you want to guarantee yourself $100,000 per year starting on your 61st birthday, how much should you save every year, for the next 20 years, starting at the end of this year. Assume that your investments are expected to yield 8% and you are likely to live till 80.
Solution:
Plot the problem in the timeline:
from 60 - 80, we know,
period = 20 years
annual payment = $100,000
rate = 8%
calculate PV at 60 using excel,
= PV (rate, nper, pmt, [fv], [type])
= PV (0.08,20,100000)
= $981,814
From 50-60,
period = 10 years
FV = $981,814
PV at 50 = ?
using excel calculator,
= PV (rate, nper, pmt, [fv],[type])
= PV (0.08,10,0,981814)
= $454,769
The timeline looks like this now,
,
From 30 - 50,
period = 20 years
FV = $454,769
annual payment = ?
rate = 8%
using excel,
= pmt (rate, nper, pv, [fv], [type])
= pmt (0.08, 20, 0, 454769)
=$9,937
Therefore, you should save $9,937 every year for the next 20 years.
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