First, draw the diagram

1. Calculate the Shortfall
2. Inflation adjust the shortfall
3. Calculate the real return and the annuity
4. Calculate the period payment

Time	25 years	30 years
Now	Retirement	Death
Return	8%	Return	7%
Inflation	2%	Inflation	2%

1. Calculate the shortfall (all on a before tax basis as stated):

The shortfall is $67,500 – $25,000 = ?

K and W’s shortfall is $42,500 before tax.

2. Calculate the inflation-adjusted shortfall (end mode):

The adjustment is PV=$42,500, I=2%, N=25, FV=?

K and W need $69,726 each year (you can round to the closest dollar)

3. Calculate the real return and annuity:

The real return is (1 + nominal return)/(1 + inflation) – 1 or (1.07)/(1.02) – 1 = ?

The real return is 4.90%.

To calculate an annuity (remember you will want the payments at the beginning of the period so use the begin mode on your calculator)

To get an annuity of $ 69,726 for 30 years at a 4.9% return, set PMT = $69,726, N = 30, I = 4.9%, and solve for PV

K and W need $1,137,074 to be available in 25 years to give us the annuity for 30 years.

4. Calculate the period payment (use end mode)

To get this future amount, we set the FV = $1,137,074, N = 25, I = 8%, and calculate the PMT = ?

K and W need to save $15,554 each year to meet their retirement goal.

 

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