SOLUTION: An investment will provide you with $100 at the end of each year for the next 10 years. What is the present value of that annuity if the discount rate is 8% annually? What is th

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Question 1114813: An investment will provide you with $100 at the end of each year for the next 10 years. What is the present value of that annuity if the discount rate is 8% annually?
What is the present value of the above if the payments are received at the beginning of each year?
If you deposit those payments ($100 at the end of each year) into an account earning 8%, what will the future value be in 10 years?
What will the future value (10 years) be if you open the account with $1,000 today, and then make the $100 deposits at the end of each year?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you want an investment to provide you with 100 dollars at the end of each year for the next 10 years.

the annual discount rate is 8% per year.

you would have to invest $671.01 today in order for that to happen.

that's the present value of that investment.

the future value of that investment would be $1,448.66.

you want an investment to provide you with 100 dollars at the begining of each year for the next 10 years.

the annual discount rate is 8% per year.

you would have to invest $724.69 today in order for that to happen.

that's the present value of that investment.

the future value of that investment would be $1,564.55.

to understand what's happening, you might want to look at the cash flows.

here they are side by side.

the remaining balance in both accounts has to be 0 at the end of the 10 year period.

if you look at the 100 deposits as a cash flow, then you can calculate the present value of those cash flows at 8% per year and the future value of those cash flows at 8% per year.

those figures are shown in the excel printout.

there are formulas that allow you to find the present value of the cash flows and the future value of the cash flows.

those formulas are in the reference below:

https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#notes

the formulas you would be looking for are:

FUTURE VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
FUTURE VALUE OF AN ANNUITY WITH BEGINNING OF TIME PERIOD PAYMENTS
PRESENT VALUE OF AN ANNUITY WITH END OF TIME PERIOD PAYMENTS
PRESENT VALUE OF AN ANNUITY WITH BEGINNING OF TIME PERIOD PAYMENTS

just follow the directions and you should be able to duplicate the figures i've given you.

if you have a problem duplicating these results using the formulas, let me know and i'll help you through them.

be sure to use the parentheses exactly as shown.
it's too easy to mess up if you don't.

there is also an online calculator that is referenced in that tutorial that allows you to calculate the present value and the future value of the annuity.

annuity is just as fancy word for regular payments.

that calculator can be found at https://arachnoid.com/finance/

i used that online calculator to get you the results shown below:

inputs for end of time period payments are shown below:

inputs for beginning of time period payments are shown below:

output for present value of end of time period payments is shown below:

output for future value of end of time period payments is shown below:

output for present value of beginning of time period payments is shown below:

output for future value of beginning of time period payments is shown below:

if you have any further questions regrding this, just let me know.