John wants to retire 30 years from now. He doesn’t know how many years he’ll actually live after he retires, so he’d like to save up enough to spend $60,000 per year forever. That way, he can never outlive his retirement savings. How much must he save every year from now until he retires in order to reach his goal? Assume his retirement savings earn 4% per year above the inflation rate.

He will need to deposit $267,451.49 each year.

Explanation:

Giving the following information:

John wants to retire 30 years from now.

He’d like to save up enough to spend $60,000 per year forever.

Interest rate= 4% per year.

The $60,000 per year forever is a perpetual annuity. First, we need to calculate the value of the annuity at the retirement age:

PV= Cf/i

Cf= cash flow

PV(retirement)= 60,000/0.04= $15,000,000

He must collect $15 million in 30 years. We need to calculate the annual deposit required to reach the goal:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

A= (15,000,000*0.04)/ [(1.04^30) - 1]

A= $267,451.49

He will need to deposit $267,451.49 each year.

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