SOLUTION: A person makes annual payments of ​$5144 into an ordinary annuity. At the end of 9 years the amount in the annuity is ​$60, 000. What annual nominal compounding rate has thi

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A person makes annual payments of ​$5144 into an ordinary annuity. At the end of 9 years the amount in the annuity is ​$60, 000. What annual nominal compounding rate has thi      Log On

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Question 1137759: A person makes annual payments of ​$5144 into an ordinary annuity. At the end of 9 years the amount in the annuity is ​$60,
000. What annual nominal compounding rate has this annuity​ earned?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i used the following online calculator to solve this.

https://arachnoid.com/finance/

you get a different answer depending on whether the payments are made at the end of the year or at the beginning of the year.

here's the results.

if the payments are made at the end of each year, the interest rate is 6.360273%.

if the payments are made at the beginning of the year, the interest rate is 5.146230%.

$$$

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$$$





Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
The formula for an Ordinary Annuity saving account compounded annually  is


    FV = P%2A%28%281%2Br%29%5En-1%29%2Fr


where FV is the future value, P is the annual payment at the end of each year, n is the number of years.


So, we need to find " r " from the equation


    %28%281%2Br%29%5E9-1%29%2Fr = FV%2FP = 60000%2F5144 = 11.664.


I used online (free of charge) solver for finding zeroes of nonlinear functions from the site 

https://www.wolframalpha.com/widgets/view.jsp?id=a7d8ae4569120b5bec12e7b6e9648b86


and got  r = 0.0636 = 6.36%.      ANSWER


CHECK.  5144%2A%28%281%2B0.0636%29%5E9-1%29%2F0.0636 = 59999.32.    ! Correct !

Solved, checked, explained and completed.


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On ordinary annuity saving plan,  see my lessons in this site

    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans