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Question 1139409: Hi first of all I want to say thank you to the tutors who have helped me so far. You all are lifesavers and I do not know what I would do without your help and this site.
I am having trouble figuring out the answer for an annuity. Can anyone help me please?
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4400 per month. You have access to an account that pays an APR of 7.2% compounded monthly.
What size nest egg do you need to achieve the desired monthly yield?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a TVM calculator should have helped you to solve this.
the online calculcator that imost always use, other than the TI Business Analyst II that i have at home, can be found at https://arachnoid.com/finance/
using this calclator, i did the f9ollowing.
you plan to work for 40 years and then retire using a 25 year annuity.
you want to arrange a retirement income of $4400 per month.
you have access to an account that pays an APR of 7.2% compounded monthly.
what size nest egg do you need to achieve the desired monthly yield?
the nest egg you need in 40 years would be the present value of the annuity.
this nest egg have to give you $4400 per month for 25 years after you retire.
using the TVM calculator i referenced, your inuts would be:
present value = 0
future value = 0
number of time periods = 25 years * 12 months per year = 300 months.
payment each month is equal to $4400.
this amount is shown as positive because it will be money coming in to you.
the present value will be shown as negative because it's money that you need to invest at the beginning of your retirement period.
interest rate per time period = 7.2% per year / 12 = .6% per month.
payment is normally at the end of each month, so that's what we'll use.
you make your inputs and you click on prevent value (pv) and the calculator tell you that the present value of the annuity needs to be equal to $611,460.42.
that's the nest egg that you have to have when you retire so you can receive a steady stream of $4400 payments at the end of each month for the next 25 years after you retire.
that nest egg needs to be there when your retirement starts.
since that's 40 years away, you need to establish an annuity that will provide you with that nest egg 40 years into the future.
you use the same TVM calculator.
this time, you make the following inputs.
present value = 0
future value = $611,460.42.
this is shown as positive because it's money that you will need to have come in to you in 40 years.
number of time periods = 40 years * 12 months per year = 480 months.
interest rate per time period = 7.2% per year / 12 = .6% per month.
payment will be made at the end of each month.
you make your inputs and click on payment (pmt) and the calculator tells you that the monthly payment needs to be $220.19
this is shown as negative because it's money that you need to spend at the end of each month for the next 40 years so that you will have $611,460.42 at the end of the investment period.
to summarize:
you invest $220.19 at the end of each month for the next 40 years.
at the end of that 40 years investment period, you will have $611,460.42.
you will invest this into a fund that will provide you with $4400 at the end of each month for the next 25 years after you retire.
i believe the solution to your problem is that you need to have a nest egg of $611,460.42 at the time that you retire.
any questions, write to dtheophilis@mail.com.
here are the results of using the online TVM calculator to solve your problem.
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