Lesson Find future value of an Ordinary Annuity saving plan

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Find future value of an Ordinary Annuity saving plan

Problem 1

You deposit $5000 at the end of each year into an account, earning 4% interest compounded annually.
How much will you have in the account in 20 years?

Solution

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = ,    (1)


where  FV is the future value of the account;  P is the annual payment (deposit); 
r is the annual percentage rate presented as a decimal; 
n is the number of deposits (= the number of years, in this case).


Under the given conditions, P = 5000;  r = 0.04;  n = 20.  So, according to the formula (1), 
you get at the end of the 20-th year


    FV =  = $148890.39.


Note that you deposit only  20*$5000 = $100,000.  The rest is what the account earns/accumulates in 20 years.

Problem 2

Eric deposits $900 at the end of each quarter to his saving account which is compounded quarterly
at 4% annual percent yield. What is the accumulated total in Eric's account at the end of 20-th year ?

Solution

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = ,    (1)


where  FV is the future value of the account;  P is your quarterly payment (deposit); 
r is the quarterly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 4, in this case).


Under the given conditions, P = 900;  r = 0.04/4;  n = 4*20 = 80.  So, according to the formula (1), Eric will get at the end of the 20-th year


    FV =  =  = $109,504.37.


Note that Eric deposits only  4*20*$900 = $72,000.  The rest is what the account earns/accumulates in 20 years.

Problem 3

Bill deposits $300 at the end of each month to his saving account which is compounded monthly
at 4% annual percent yield. What is the accumulated total in Bill's's account at the end of 20-th year ?

Solution

It is a classic Ordinary Annuity saving plan. The general formula is 


    FV = ,    (1)


where  FV is the future value of the account;  P is your monthly payment (deposit); 
r is the monthly percentage yield presented as a decimal; 
n is the number of deposits (= the number of years multiplied by 12, in this case).


Under the given conditions, P = 300;  r = 0.04/12;  n = 12*20 = 240.  
So, according to the formula (1), you get at the end of the 20-th year


    FV =  =  = $110,032.39.


Note that Bill deposits only  12*20*$300 = $72,000.  The rest is what the account earns/accumulates in 20 years.

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To make such complicated calculations as they are in this problem,
you should have/use an appropriate calculator for such long formulas.

Ideal choice is MS Excel, if you have it in your computer.

Then you write a formula in a text editor, copy-paste it
into an Excel work-sheet cell and click "Enter" - the result is ready
in the next second.

If you have no MS Excel in your computer, you may find similar
free of charge calculators in the Internet. One such calculator is

www.desmos.com/calculator

It allows you to do the same thing: you write a formula in a text editor,
copy-paste it into this calculator and click "Enter" - the result is ready
in the next instance.

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On Ordinary Annuity saving plans, see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.

These lessons contain EVERYTHING you need to know about this subject, in clear and compact form.
When you learn from these lessons, you will be able to solve similar problems and to perform similar calculations
in semi-automatic mode.

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 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
    - Find the compounding rate of an ordinary annuity
    - 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.

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