Question

# How much must you deposit each year into your retirement account starting now and continuing through...

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.

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