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