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 sec

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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 sec

urity 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?

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1 answer:

harina [3.8K] · Answer 1 · 2026-04-01T21:43:05+03:00

To receive monthly income, adjust the interest rate and duration variables for the investment to a monthly timeframe; From the total of $12,000, calculate Jenny's personal savings after removing social security payments and her pension benefits; = 12,000 - 3,000 - 4,000 = $5,000. This recurring 5,000 will be the PMT for the annuity calculation. If the marginal tax rate is 28%, determine the nominal rate after tax; Pre-tax nominal rate = 7.9% or 0.079. The after-tax nominal rate = (1-0.28) * 0.079 = 0.05688 or 5.688%. Next, find the real interest rate using the Fisher equation applicable to the nominal and inflation rates: Real rate = [(1+Nominal) / (1+inflation)] -1 = [(1+0.05688) / (1+0.026)] -1 = 1.0301 -1 = 0.0301. Thus, the real rate is 3.01%. Now, using a financial calculator, input the following: N = 95 - 70 = 25 years, converted to months = 25*12 = 300. I/Y = 3.01% /12 = 0.2508%. PMT = 5,000, FV = 75,000*6 = 450,000. Then calculate PV = $1,265,460.78. Therefore, she should aim to save $1,265,460.78.