# 3.0 Introduction

## Chapter Learning Objectives

By the end of the chapter you should be able to:

- Construct a full or partial amortization schedule for a loan
- Calculate the principal and interest components of any payment
- Calculate the loan balance after any payment
- Calculate the total principal paid and total interest paid for a series of payments
- Calculate the final payment for a loan
- Calculate mortgage payments for the initial term and renewal term
- Calculate amortization periods to reflect changes in payment frequency
- Calculate mortgage balances and amortization periods to reflect prepayments of principal

It would be nice to pay cash for everything that you acquire. However, goods such as housing, automobiles, furniture, and electronics require more money than most Canadians have lying around. If you tried saving up and paying cash for these large purchases, it would take a long time to accumulate enough funds. Take the example of a new home. If you saved [latex]\$300[/latex] per month at [latex]5\%[/latex] compounded annually, it would take approximately 30 years to save up [latex]\$250,000[/latex] in cash, and in the meantime, of course, you would still need to pay for somewhere to live.

So it is not necessarily bad to borrow money at some point. However, to borrow wisely you had better understand where your money is going. Would it shock you to learn that in a typical mortgage arrangement most homeowners pay approximately double for their homes? That is, [latex]\$250,000[/latex] for the home and [latex]\$250,000[/latex] in interest!

Businesses borrow money for many of the same reasons as consumers. Loans and mortgages in the business world are commonplace. Certain business activities need to be financed upfront. For example, new products must be researched and developed before a single unit can be sold to consumers. Research and development requires investments that will not be reimbursed until the products turn a profit. All company debts must be accurately recorded onto balance sheets to reflect the balances owing. Income statements must appropriately track interest expenses or earnings. Because businesses can deduct their interest expenses against corporate taxable income and lower their taxes, it is important to see what proportion of their loan payments is going to interest.

When you take out a mortgage for yourself or your business, where does your money go? You need a chart of your loan payments showing how much interest the bank charges and how much is applied against your principal. This chapter takes you through calculating the balance, the principal and interest components of any single payment for a loan. You will now see how to calculate the final payment for a loan. Finally, you will be guided through the largest transactions you personally are likely to make: basic mortgages and renewals.

#### Attribution

“Chapter 13 Introduction” from Business Math: A Step-by-Step Handbook Abridged by Sanja Krajisnik; Carol Leppinen; and Jelena Loncar-Vines is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

“Chapter 13 Introduction” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.