Question

How much must you deposit each year into your retirement account starting now and continuing through year 10 if you want to be able to withdraw $90,000 per year forever, beginning 27 years from now? Assume the account earns interest at 13% per year.

Answer 1

R= 13%

If funds of $90000 are withdrwan for perpetuity begining 27 years from now.

then,

funds required at 27 years from now= 90000/13%

$ 692307.69

Now, let annual deposits for 10 years= P

then,

692307.69= (p*[(1+i^n-1)/i]*(1+i^y-n+1)

692307.69= (p*[(1+0.13^10-1)/0.13]*(1+0.13^27-11)

692307.69= p*(23.108)*(7.067)

692307.69= p*163.304

p= 692307.69/163.304

p=4239.37

annual deposit required $4239.37

SECOND METHOD

withdrwalable ammount after 27 years= $90000

i= 13%

First we will find the perpetual stream inflow of $90000 at 13% amd then find thepresent value at the end of 10th year and the annual deposit of that ammount for 11 years ( from year 0 to year 10)

Ammount= withdrawable ammount after 27 years/i(p/f, i, 12)(a/f, 13%, 11)

Ammount= 4239.37