Question 1065758
they plan to retire at 60 and expect to live until 90.
that means they need enough money for 30 years.


they believe they can earn 4% per year.
divide that by 4 and it becomes 1% per quarter.


they will pay themselves 12,000 at the beginning of each quarter.


thy will need 844,770.327 in their account at the beginning of their retirement period.


i used an online time value of money calculator to come up with this amount.


the online calculator i used is at <a href = "http://arachnoid.com/finance/" target = "_blank">http://arachnoid.com/finance/</a>


my inputs and outputs are shown below:


first the inputs.


<img src = "http://theo.x10hosting.com/2017/012704.jpg" alt="$$$" </>


next the outputs.


<img src = "http://theo.x10hosting.com/2017/012705.jpg" alt="$$$" </>


the inputs were:


present value = 0
future value = 0
number of periods = 30 years * 4 quarters per year = 120 quarters.
payment amount = 12,000 per qusarter.
interest rate per period = 4% per year divided by 4 quarters per year = 1% per quarter.
payment is at the beginning of each quarter.


the outputs are the present value of 844,770.33 which gets displayed after i select the compute pv button.


this can also be done manually using financial formulas.


i have a list of these formulas.


they can be found at <a href= "https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas" target = "_blank">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#formulas</a>


the formula you want would be:


PRESENT VALUE OF AN ANNUITY WITH BEGINNING OF TIME PERIOD PAYMENTS


that formula will be:


PRESENT VALUE OF AN ANNUITY WITH BEGINNING OF TIME PERIOD PAYMENTS 

p = ((a*(1-1/(1+r)^n))/r)*(1+r) 

p is the present value of the annuity.
a is the annuity.
r is the interest rate per time period.
n is the number of time periods. 


a is 12,000.
r is .01
n is 120


you would get p = ((12000*(1-1/(1+.01)^120))/.01)*(1+.01)


you should get p = 844770.327 rounded to 3 decimal places.