CHAPTER 5

Mathematics of Individual Finance

[Mathematics of Individual Finance Page 1] [Time Value Of Money][Future Values] [More Frequent Compounding] [Effective Annual Interest Rate] [Present Value]
[Annuities] [Present Value Of An Annuity] [Annuities Due] [Future Value Of An Annuity] [Determining Payments] [Bond Valuation]
[Uneven Cash Flows] [Amortization Schedule] [Household Capital Budgeting] [Duration] [Summary] [Discussion Questions]
[Problems]

Amortization Schedules

When you are repaying an amortized loan such as a mortgage and an installment loan, it is often necessary to calculate the amount of interest you have paid in a given period, for tax reasons, or the remaining balance on the loan in the event that you want to refinance it or borrow against the equity. Calculating an amortization schedule without a computer or a specialized calculator is tedious and time-consuming but is relatively straightforward. You merely calculate the interest for the first period, subtract that from the amount of the payment, and the difference is amortization which reduces the principal. A simple example will show how it is done.

Example 5-19

Josh takes out a five year auto loan for $10,000 which calls for annual payments at a rate of 10%. Calculate his annual payment, his annual interest payments and his balance at the end of each year.

Solution 5-19

First, his payment is equal to the payment on an annuity of 5 years at 10% with a present value of $10,000 which is $2,637.97. Then we set up a table similar to the following:

PERIODBEGINNING BALANCEINTEREST AT (1O%)AMORTIZATION PAYMENT-INTEREST
1$10,000.00$1000.00$1637.97
2$8,362.03$836.20$1,801.67
3$6,560.26$656.03$1,981.94
4$4,578.32$457.83$2,180.14
5$2,398.18$239.81$2,398.15

In spite of rounding error, we end up within 3 cents of the correct final balance. Many calculators are programmed to give you the balance or interest as of a certain payment, saving the tedium of setting up such a table. Of course, this is an ideal job for a spreadsheet which handles repetitive processes without complaint. Another quick method of solving for the principal at the end of n periods is through the following formula:

P = (C/r)[1-1/(1+r)n]

Equation 5-9

where

C is the cash flow payment

P is the principal

r is the interest rate

n is the number of payments remaining

In our example illustrated above, the remaining principal at the end of the second period would be:

P= (C/r)[1-1/(1+r)n]
= ($2,637.97/.1)[1-1/(1.1)3]
= ($26,379.70)[1-1/1.331]
= ($26,379.70)[.2486852]
= $6,560.24

[Household Capital Budgeting]

[Back to College of Business Administration Homepage]

Copyright © 1996 Marquette University -- All rights reserved. The Marquette University logo is a trademark and is meant for viewing purposes only. Questions, comments or suggestions to webmaster Last update: October 9th, 1996

Marquette University

* P.O.Box 1881 * Milwaukee, WI
53201-1881

This page was programmed by Jim Schutte