Jenny wants a monthly retirement income of $12,000. She will retire on her birthday at age 70 with a $3,000 per month social security monthly benefit and a $4000 per month defined benefit pension.

She expects to die on her birthday at age 95 and would like to leave $75,000 to each of her 6 children.

She expects a 7.9% annual return on her Roth 401k. She expects a 2.6% annual rate of inflation.

How much will she need to have saved to invest when she retires?

Since she wants to receive the income per month, change the interest rate and duration on investment variables to monthly basis;

Out of the $12,000, find Jenny's own savings after deducting social security income & Pension benefit;

= 12,000 - 3,000 - 4,000 = $5,000

Since the 5,000 is recurring, it will be the PMT in annuity calculation.

If marginal tax rate = 28%, find the aftertax nominal rate;

Pretax nominal rate = 7.9% or 0.079

After tax nominal rate = (1-0.28) * 0.079

After tax nominal rate = 0.05688 or 5.688%

Next, find the real interest rate using Fisher equation that applies the nominal rate and inflation rate

Real rate = [ (1+Nominal) / (1+inflation) ] - 1

=[ (1+0.05688) / (1+0.026) ] - 1

= 1.0301 - 1

= 0.0301

Real rate = 3.01%

Next, using financial calculator, enter the following inputs;

N = 95 - 70 = 25 years, but convert to months = 25*12 = 300

I/Y = 3.01% / 12 = 0.2508%

PMT = 5,000

FV = 75,000*6 = 450,000

then CPT PV = $1,265,460.78

Therefore, she need to have saved $1,265,460.78