Question

Mike wants to receive $40,000 per year pretax from his investments for the next 30 years. He is concerned about inflation, which he expects to average 3 percent. He can earn a pretax rate of 6 percent on his money. How much does he need in an account to generate $40,000 in annual inflation-adjusted income (payments at the end of each year)?  

Answer 1

The effective interest rate for this investment (annual inflation-adjusted interest rate)

= [(1+ Nominal interest rate)/ (1+ Inflation rate)]-1

Where,

Nominal interest rate= 6% per year

Inflation rate = 3% per year

Therefore,

The effective interest rate for this investment = [(1+ 6%)/ (1+ 3%)]-1 = 0.0291 or 2.91% per year

Now we can calculate the amount need in an account to generate $40,000 in annual inflation-adjusted income (payments at the end of each year) with the help of following present value (PV) of annuity formula.

PV = PMT * [1-(1+i) ^-n)]/i

Where,

Present value (PV) =?

PMT = annual payment =$40,000

n = N = number of payments = 30 years

i = I/Y = effective interest rate per year or discount rate = 2.91%

Therefore,

PV = $40,000 * [1- (1+2.91%) ^-30]/2.91%

= $792,947.58 (rounded off to two decimal points)

The amount need in an account to generate $40,000 in annual inflation-adjusted income is $792,947.58