Question

you put aside 100,000 in year t=0 and let it grow at 5.8% interest for 5 years. exactly one year after that you start to withdraw your money for 3 years in equal amounts until it is exhausted. How much can you withdraw per year?

Answer 1

Initial Deposit = $100,000.
No of years = 5 years
Interest Rate = 5.8%

Calculation of the amount we will have after 5 years.

Future value formula is given by

FV = ΣPV (1+ r)n
where FV = Future value
PV = Present Value
r = Interest Rate
n = Number of times interest applied per time period
            

Therefore FV5 = PV0 (1+r)5
FV5 = 100,000 * (1+.058)5
   FV5 = 100,000 * (1.058)5
   FV5 = 100,000 * 1.32564835
   FV5 = 132,564.84 (Rounded off)
                  

So we will have $132,564.84 after 5 years from now.
Now we will withdraw equal amount of money for next 3 years.

In financial terms,
PV = $132,564.84
Interest Rate = 5.80%
No of Years = 3

We have to find equal annual withdrawl or PMT.

By using the formula to calculate PMT in excel. The formula is
=PMT(Rate, NPer, Present Value, Future Value, Type)
where,
Rate = Interest Rate
NPer = No of Periods    
Type is 0 if PMT are made on the end of year and 1 if the payments are made at the beginning of year.

Using the formula
PMT = $49,410.40 (rounded off)

So the withdraw amount will be $49,410.40 per year.