Explanation of the Topic...

Present Value of an
Ordinary Annuity

Print  Email
Facebook Logo

Calculating the Payment in an Ordinary Annuity (PMT)

Present value calculations allow us to determine the amount of the recurring payments in an ordinary annuity if we know the other components: present value, interest rate, and the length of the annuity. Exercises 5 and 6 will demonstrate how to solve for the payment amount.



Exercise #5. On June 1, 2008, Grandma deposits $1,733 into an account to help pay for Emily's summer volleyball camp for four consecutive years. The first camp is scheduled for June 2009. The account earns 6% interest per year, compounded annually. The interest earned on the account balance is deposited into the account on May 31 of each year. If Grandma wants the balance to be $0 at the end of the four years, how much should she withdraw for Emily each June?

The following timeline helps us visualize the facts:

PVOA= $1,733






PMT=?? PMT=?? PMT=?? PMT=??







1 year 1 year 1 year 1 year
6/1/08 6/1/09 6/1/10 6/1/11 6/1/12
0 1 2 3 4

n = 4 years;  i = 10% per year


Calculation of Exercise #5 using the PVOA Table
Using the above information and factors from our PVOA Table, we can solve for the unknown payment amount (PMT) as follows:

PVOA   =   PMT times [ PVOA factor for n = 4 years; i = 6% per year ]
$1,733   =   PMT times [ 3.465 ] ← PVOA Factor for n = 4; i = 6% from PVOA Table
$1,733 / 3.465   =   PMT
$500   =   PMT


We use simple algebra and the appropriate present value factor to determine that Grandma can withdraw $500 each June 1 beginning in 2009.

The following table shows the account activity, confirming that $500 can be withdrawn each year for four years:
Date Amount Deposited Interest Added* Amount Withdrawn Account Balance
June 1, 2008 $  1,733.00

$  1,733.00
May 31, 2009
103.98
1,836.98
June 1, 2009

500.00 1,336.98
May 31, 2010
80.22
1,417.20
June 1, 2010

500.00 917.20
May 31, 2011
55.03
972.23
June 1, 2011

500.00 472.23
May 31, 2012
28.33
500.56
June 1, 2012

500.00 0.56

    * 6% of previous account balance




Exercise #6. Your company plans to borrow $10,152 on January 1, 2008. You would like to repay the loan by making six semiannual loan payments beginning on June 30, 2008. The payments will be equal amounts and will cover a portion of both the interest (10% per year compounded semiannually) and the principal repayment. The payments will be paid on each June 30 and December 31. What will be the amount of each of the six payments?

Calculation of Exercise #6 using the PVOA Table
Our first step is to construct a timeline to organize the information:

PVOA= $10,152






PMT=?? PMT=?? PMT=??


PMT=??





.....


6 months 6 months 6 months


6 months
01/01/08 6/30/08 12/31/08 6/30/09
6/30/10 12/31/10
0 1 2 3

5 6

n = 6 semiannual periods;  i = 5% per semiannual period


Using the above information and factors from our PVOA Table, we can solve for the unknown payment amount (PMT) with the following equation:

PVOA   =   PMT times [ PVOA factor for n = 6 semiannual periods; i = 5% per semiannual period ]
$10,152   =   PMT times [ 5.076 ] ← PVOA Factor for n = 6; i = 5% from PVOA Table
$10,152 / 5.076   =   PMT
$2,000   =   PMT


We use simple algebra and the appropriate present value factor to determine that each of the six payments will be $2,000. The first payment will be made on June 30,2008 and the final payment will occur on December 31, 2010.

The following loan amortization schedule shows the amount of interest and principal contained in each loan payment and confirms that the loan will be paid by December 31, 2010.
   Loan Amortization Schedule
   (For $10,152.00 at 10% per year with 6 semiannual payments.)

Pmt No. Date Total Payment Interest Payment* Principal Payment** Principal Balance

Jan. 1, 2008


$  10,152.00
1 June 30, 2008 $  2,000.00 $  507.60 $  1,492.40 $  8,659.60
2 Dec. 31, 2008 2,000.00 432.98 1,567.02 7,092.58
3 June 30, 2009 2,000.00 354.63 1,645.37 5,447.21
4 Dec. 31, 2009 2,000.00 272.36 1,727.64 3,719.57
5 June 30, 2010 2,000.00 185.98 1,814.02 1,905.55
6 Dec. 31, 2010 2,000.00 95.28 1,904.72 0.83

   * Interest payment equals 5% of the previous principal balance.
   ** Principal payment equals $2,000 minus interest payment.



   Download and Print our Complete Learning Package
Complete PDF Package

Now you can highlight, make notes, and study away from your computer.
Includes bonus materials not available on our website.
Click Here to Learn More




  Part 1    Part 2    Part 3    Part 4    Part 5    Part 6    Part 7    Part 8        To Top





Accounting
Cheat Sheet

Receive our popular 15-page
Cheat Sheet at no cost when
you join our free newsletter:


First Name:
Email Address:
60,000+ have already joined
We keep your email address
100% safe and secure.

Download our new
Business Forms
Learn more about a
Career in Accounting
Start a discussion in our Accounting Forum






Most Recent Questions for this Topic




Why AccountingCoach.com?

the accounting coach

AccountingCoach.com is designed to help people without an accounting background easily understand accounting concepts at no cost.


By investing thousands of hours, we have created clear and concise accounting information for both business people and students of all ages.


We understand how difficult accounting can be. That's why each accounting topic includes a clear explanation, reinforcing drills, Q&A, puzzles, dictionary of terms, etc.


» Read 1,200+ Visitor Testimonials