Question

Tom and Debbie are starting to take their retirement planning seriously. They are both 46 and plan to retire in 20 years at the age of 66. They expect to live 15 years in retirement (a life expectancy of 81). Between their 401k and IRA accounts they currently have $67,966 in retirement savings.

They currently have a combined income of $88,000 per year and expect to be able to live comfortably in retirement with 80% of their current purchasing power. They expect inflation to be 2% per year for the rest of their lives. They also expect to earn 11.0% per year (the average return on Blue Chip stocks) on their investments, both now and in retirement.

What amount of annual income will they need (after adjusting for inflation) in each of the fifteen years of retirement to have the purchasing power of 80% of their current income? Assuming they will continue to earn 11.0% on their investments, how much money will they need to have in their retirement accounts when they retire so that it will provide the fifteen years of income? (note: at the end of the 15 years the account balance should be zero.) Taking into account what they currently have in savings, how much will they have to save each month to meet their retirement needs? Sensitivity analysis: Redo the analysis assuming that they only earn 9% on their investments, instead of 11.0%. Determine the needed amounts so they have the money they need in retirement.

Answer 1

Current Age	46
Expected Retirement Age	66
1. No. of years to retirement	20
Life Expectancy	81
2. No. of years after retirement	15
Rate of return during accumulation	11%
Rate of return after retirment	11%
inflation rate	2%
3. Inflation adjusted rate	8.8%

4. Post retirement requirements or expected expenditures (inflation adjusted):

Current Income = $88000 PA

After retirement requirements @80% of current income = $70400 PA

inflation rate = 2%

Expenses at retirement (inflation adjusted) = FV of $70800 @ 2%

=> 70800 * (1.02)²⁰

=> $105205 PA

5. Retirement Corpus:-

Post retirement annual required funds = 105205 (as calculated in step 4)

No. of years after retirement = 15

inflation adjusted rate = 8.8%

Corpus required = PV of 105205 @ 8.8%

=> 105205 [{1-(1.088)^-25} / 0.088]

=> 858130

5. Monthly savings to meet their retirement needs:-

No. of years for retirement = 20 => 20*12 = 240 months

rate of return = 11% => 11/12 = 0.9167%

Required Corpus = $858,130 (as calculated in step 4)

Current savings = $  67,966

Amount required = $790164

Monthly savings = PMT of PV of 858130 @ 0.9167% for 240 months

=> 790164 = PMT [{(1.0092)²⁴⁰ - 1} / 0.0092]

=> $912