Chapter 4: Managing Your Money Lecture notes Math 1030 Section DSection D.1: Loan BasicsDefinition of loan principalFor any loan, the principal is the amount of money owed at any particular time. Interest is charged onthe loan principal. To pay off a loan, you must gradually pay down the principal. Thus, in general, ev-ery payment should include all the interest you owe plus some amount that goes toward paying off theprincipal.Ex.1Suppose you borrow $1200 at an annual interest rate APR= 12% (or 1% per month). At the end of thefirst month, you owe interest in the amount ofIf you paid only this $12 in interest, you would still owe $1200. That is, the loan principal would still be$1200. In that case you would owe the same $12 in interest the next month and this can go on forever.If you hope to make progress in paying off the loan, you need to pay part of the principal as well asinterest. For example, suppose that you paid $200 toward your loan principal each month, plus thecurrent interest. At the end of the first month, you would pay $200 toward principal, plus $12 for the 1%interest you owe:Because you have paid $200 toward principal, your new loan principal would beAt the end of the second month, you would again pay $200 toward principal and 1% interestThe table shows how the calculations continue until the loan is paid after 6 months.AFTER N MONTHS PRIOR PRINCIPAL INTEREST TOTAL PAYMENT NEW PRINCIPAL1 $1200 1% × 1200 = 12 200 + 12 = 212 $10002 $1000 1% × 1000 = 10 200 + 10 = 210 $8003 $800 1% × 800 = 8 200 + 8 = 208 $6004 $600 1% × 600 = 6 200 + 6 = 206 $4005 $400 1% × 400 = 4 200 + 4 = 204 $2006 $200 1% × 200 = 2 200 + 2 = 202 $01Chapter 4: Managing Your Money Lecture notes Math 1030 Section DInstallment loan and loan payment formulaThere is nothing wrong with this method of paying off a loan, but most people prefer to pay the same totalamount each month because it makes planning a budget easier. A loan that you pay off with equal regularpayments is called installment loan (or amortized loan). The regualr payment amount can be computedusing the loan payment formula:PMT =P ×APRnh1 −1 +APRn(−nY )iwhereP MT = regular payment amountP = starting loan principal (amount borrowed)AP R = annual percentage rate (as a decimal)n = number of payment periods per yearY = loan term in yearsEx.2What is the regular payment amount in Example 1?2Chapter 4: Managing Your Money Lecture notes Math 1030 Section DPrincipal and interest payments.Because the loan principal is gradually paid down with the installment payments, the interest due eachmonth must also decline gradually. Thus, because the payments remain the same, the amount paid towardprincipal each month gradually rises. Therefore, the portions of installment loan payments going towardprincipal and toward interest vary as the loan is paid down. Early in the loan term, the portion goingtoward interest is relatively high and the portion going toward principal is relatively low. As the termproceeds, the portion going toward interest gradually decreases and the portion going toward principalgradually increases.Ex.3 Student loan.Suppose you have student loans totaling $7500 when you graduate from college. The interest rate is APR= 9% and the term is 10 years. What are your monthly payments? How much will you pay over thelifetime of the loan? What is the total interest you will pay on the loan?3Chapter 4: Managing Your Money Lecture notes Math 1030 Section DEx.4 Principal and interest payments.For the loan in Example 3, calculate the portions of your payments that go to principal and to interestduring the first 3 months.4Chapter 4: Managing Your Money Lecture notes Math 1030 Section DChoices of rate and termChoices of rate and term.You will usually have several choices of interest rate and loan term when seeking a loan. Thus, you willhave to evaluate your choices and make the decision that is the best for your personal situation.Ex.5You need a $6000 loan to buy a used car. Your bank offers a 3-year loan at 8%, a 4-year loan at 9%, anda 5-year loan at 10%. Calculate your monthly payments and total interest over the loan term with eachoption.5Chapter 4: Managing Your Money Lecture notes Math 1030 Section DSection D.2: Credit CardsCredit card loansCredit card loans differ from installment loans in that you are not required to pay off your balance in any setperiod of time. Instead, you are required to make only a minimum monthly payment that generally coversall the interest but very little principal. As a result, it takes a very long time to pay off your credit cardloan in a particular amount of time. You should use the loan payment formula to calculate the necessarypayments.Ex.6You have a credit card balance of $2300 with an annual interest rate of 21%. You decide to pay off yourbalance in 1 year. How much will you need to pay each month? Assume you make no further credit cardpurchases.6Chapter 4: Managing Your Money Lecture notes Math 1030 Section DEx.7Paul has gotten into credit card trouble. He has a balance of $9500 and just lost his job. His credit cardcompany allows him to suspend his payments until he finds a new job, but continues to charge interest.If it takes him a year to find a new job and his credit card company charges interest of APR = 21%compounded daily, how much will he owe when he starts his new job?7Chapter 4: Managing Your Money Lecture notes Math 1030 Section DSection D.3: MortgagesMortgagesOne of the most popular types of installment loans is designed specifically to help you buy a home. Itis called mortgage. Mortgage interest rates generally are lower than interest rates on other types of loansbecause your home itself serves as a payment guarantee. If you fail to make your payments, the lender(usually a bank or a mortgage company) can take possession of your home and sell it to cover the amountloaned to you.There are several considerations in getting a home mortgage. First, the lender will probably require a downpayment, typically 10% or 20% of the purchase price. Then the lender will loan you the rest of the moneyneeded to purchase the home.Most lenders also charge fees, or closing costs, at the time you take out the loan. Closing costs can besubstantial and may vary significantly between lenders, so you should be sure that you understand them.There are two types of closing costs:• Direct fees, such as fees for getting the home appraised and checking your credit history, for whichthe lender charges a