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Present Value of an Annuity:

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Learning objectives of this article:

  1. Define a explain the present value of an annuity.
  2. How is it calculated?
  3. What are the benefits of its calculation?

Contents:

Definition and Explanation:

The present value of an annuity is an amount of money today which is equivalent to a series of equal payments in the future. For example, you have won a lottery and lottery officials give you the choice of having a lump-sum payment today or a series of payments at the end of each of the next 5 years. The two alternatives would be considered equivalent (in a monetary sense) if by investing the lump-sum today you could generate (with accumulated interest) annual withdrawal equal to five installments offered by the lottery. An assumption is that the final withdrawal would deplete the investment completely. Consider the following example.

Formula:

Following formula is use for the calculation of present value of an annuity:

  • R = Amount of an annuity
  • i = interest rate per compounding period
  • n = Number of annuity payments (also, the number of compounding periods)
  • Present value of the annuity

Example:

A person recently won a state lottery. The terms of the lottery are that the winner will receive annual payments of $20,000 at the end of this year and each of the following 3 years. If the winner could invest money today at the rate of 8 percent per year compounded annually, what is the present value of the four payments?

Solution:

  • i = 0.08
  • n = 4
  • R = $20,000

The present value of the four payments is calculated as follows:

A = $20,000(3.31213*)

= $66,242.6

*Present value of an ordinary annuity table

Determining the Size of Annuity:

There are problems in which we may be given the present value of an annuity and need to determine the size of the corresponding annuity. For example, given a loan of $10,000 which is received today, what quarterly payments must be made to repay the loan in 5 years if interest is charged at the rate of 10 percent per year, compounded quarterly? The process of repaying loan by installment payments is referred to as amortizing a loan.

To determine the size of an annuity, the formula is solved for R:

The quarterly payment necessary to repay the above motioned $10,000 is calculated as follows:

  • A = $10,000
  • i = 0.10/4 = 0.025
  • n = 20

R = $10,000/15.58916*

= $641.50

*Present value of an ordinary annuity table

There will be 20 payments totaling $12,830; thus interest will equal $2,830 on the loan

 

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More study material from this topic:

Methods for the evaluation of capital investment analysis
Average rate of return or accounting rate of return method
Cash payback method
Net present value method
Internal rate of return method
Simple interest
Future value of a single sum
Future value of an annuity
Present value of a single sum
Present value of an annuity
Qualitative consideration in capital investment analysis
Capital investment analysis and unequal proposal lives
Capital rationing decision process
Difference between simple interest and compound interest
Difference between nominal and effective interest rate
Future value of $1 table
Present value of $1 table
Present value of ordinary annuity table
Future value of ordinary annuity table

 

A D V E R T I S E M E N T

 

Financial Accounting Topics


  Introduction to Accounting
 ----------------------------------------------------------------------------
  Transactions and Accounting Equation
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  Analysis of Business Transactions
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  Journal, Ledger and Trial Balance
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  Accounting for Bills of Exchange
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  Special Journals
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  Cash Book
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Bank Reconciliation Statement
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  Final Accounts
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  Work Sheet
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  Capital and Revenue Items
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  Valuation of Inventories
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  Accounts of Non-profit Making Organizations
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  Statement of Cash Flows
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  Accounting Ratios Analysis
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  Depreciation, Provisions and Reserves
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  Accounting Dictionary
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  Financial Calculators
 
 
 
Managerial Accounting Topics

  Financial Statements
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  Cost Volume Profit Relationship
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  Variable Costing System
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  Materials and Inventory Cost Control
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  Activity Based Costing System
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  Standard Costing and Variance Analysis
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  Balanced Scorecard
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  Capital Investment Analysis/Capital Budgeting
 

 

 

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