Lesson Find the compounding rate of an ordinary annuity

Algebra ->  Finance -> Lesson Find the compounding rate of an ordinary annuity      Log On


   

This Lesson (Find the compounding rate of an ordinary annuity) was created by by ikleyn(52803) About Me : View Source, Show
About ikleyn:

Find the compounding rate of an ordinary annuity


Problem 1

To save for​ retirement,  Karla  Harby put ​ $500 each month into an ordinary annuity for  10  years.
Interest was compounded monthly.  At the end of the  10  ​years,  the annuity was worth ​ $84,608.
What annual interest rate did she​ receive?

Solution 

Use the formula for the future value of the ordinary annuity

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


where r is the effective monthly rate of compounding, n the number of deposits ( = months, in this problem).


Substitute the numbers

    84608 = 500%2A%28%28%281%2Br%29%5E120-1%29%2Fr%29.


Simplify

    84608%2F500 = %28%281%2Br%29%5E120-1%29%2Fr,

or

    %28%281%2Br%29%5E120-1%29%2Fr = 169.216.


It is the equation, which you want to solve to find r.


Use any online solver for transcendent equations, for example, at this site www.desmos.com/calculator


The solution is r = 0.00549  as the effective monthly rate.


So, the annual nominal rate is  0.00549*12 = 0.06588,  or  6.588%.    <<<---===  highlight%28highlight%28ANSWER%29%29.


CHECK.  Substitute this value of annual nominal rate into the formula for the future value.

         You will get  FV = 500%2A%28%28%281%2B0.06588%2F12%29%5E120-1%29%2F%28%280.06588%2F12%29%29%29 = $84,607.76, which is close to the given value in the problem.


My other lessons on Finance problems in this site are
    - Problems on simple interest accounts
    - Problems on discretely compounded accounts
    - Problems on continuously compounded accounts
    - Find future value of an Ordinary Annuity
    - Find regular deposits for an Ordinary Annuity
    - How long will it take for an ordinary annuity to get an assigned value?
    - Find future value for an Annuity Due saving plan
    - Regular withdrawals from an annuity account
    - Ordinary annuity account with non-zero initial deposit as a combined total of two accounts
    - Annual depositing and semi-annual compounding in ordinary annuity saving plan
    - Variable withdrawals from a compounded account (sinking fund)
    - Present value of an ordinary annuity cumulative saving plan
    - Problems on sinking funds
    - Accumulate money using ordinary annuity; then spend money via sinking fund
    - Calculating a retirement plan
    - Accumulating money via ordinary annuity and spending simultaneously via sinking fund
    - Loan problems
    - Mortgage problems
    - Amortizing a debt on a credit card
    - One level more complicated non-standard problems on ordinary annuity plans
    - One level more complicated problems on sinking funds
    - One level more complicated non-standard problems on loans
    - Using Excel to find the principal part of a certain loan payment
    - Using Excel to find the interest part of a certain loan payment
    - Tricky problems on present values of annuities
    - OVERVIEW of my lessons on Finance section in this site

Use this file/link  ALGEBRA-I - YOUR ONLINE TEXTBOOK  to navigate over all topics and lessons of the online textbook  ALGEBRA-I.

Use this file/link  ALGEBRA-II - YOUR ONLINE TEXTBOOK  to navigate over all topics and lessons of the online textbook  ALGEBRA-II.


This lesson has been accessed 374 times.