Our local barber wants to retire at 65 and have $1,000,000 in his retirement fund. He also wants to withdraw perpetual annuity payments, when he retires, for the rest of his life. He initially deposits $25,000 at the age of 35 and $7,500 thereafter at the beginning of each year for the next 30 years.
What would the annual perpetual annuity payments of our barber be at his retirement age of 65? Thank you for any help.
The main concern we have in solving this problem is to find the interest rate. But, since you have 4 out of 5 variable, that is: FV=$1,000,000, PV=$25,000, Periodic Payments=$7,500 each, and N=30 Number of periods, then its relatively simple to find the interest rate using iteration. We could try a rate that will equate the FV of $25,000 Plus the FV of the stream of payments to =$1,000,000.
But modern computers and calculators can find such rate almost instantaneously once we enter all the variable we have accurately. For that purpose, I shall use this fine online calculator to do that:
We simply enter $1,000,000 under FV, $25,000 as (-) under PV, $7,500 also as (-) under PMT and 30 under NP. The two negative ones are "Payments made or owed". Then we simply press "IR", or Interest rate and it instantly gives us the Interest Rate we are after. Keep in mind that we have to use the "beginning" instead of the "End" of the periods since they are made at the beginning of the year.
Once we enter them and press "IR", it instantly gives us a rate of:7.254922%
And now it becomes a simple matter of finding his "Perpetual Payment", by simply multiplying this by his $1,000,000 as follows: $1,000,000 x $7.254922% =$72,549.22 - his annual perpetual payment.
P.S. Learn to use the above online calculator to solve virtually all the TVM problems that you may have.