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Chapter 11 – Consumer Mathematics 11.1 – Percentages 11.2 – Personal Loans and Simple Interest The money the bank is willing to lend the consumer is called the principal of the loan. The amount of credit and the interest rate that you may obtain depend on the assurance that you can give the lender that you will be able to repay the loan. Security (collateral) is anything of value pledged by the borrower that the lender may sell or keep if the borrower does not repay the loan. I.e., a business, a mortgage on a property, the title to an automobile. The borrower must sign an agreement called a personal note which is a document that states the terms and conditions of the loan. Interest is the money the borrower pays for the use of the lender’s money. One type of interest is called simple interest. Simple interest is based on the entire amount of the loan for the total period of the loan. Simple Interest Formula Interest principal rate time i prt Ordinary Interest The most common type of simple interest is called ordinary interest. For computing ordinary interest, each month has 30 days and a year has 12 months or 360 days. On the due date of a simple interest note the borrower must repay the principal plus the interest. There is another type of loan, the discount note, for which the interest is paid at the time the borrower receives the loan. The interest charged in advance is called the bank discount. 11.3 Compound Interest An investment us the use of money or capital for income or profit. Investments can be separated into two classes: fixed investments and variable investments. In a fixed investment, the amount invested as principal is guaranteed and the interest is computed at a fixed rate. Examples of fixed investments are savings accounts and certificates of deposit (cds). In a variable investment, neither the principal nor the interest is guaranteed. Examples of variable investments are stocks and mutual funds. The interest paid on savings accounts at most banks is compound interest. A bank computes the interest periodically (for example, daily or quarterly) and adds the interest to the original principal. The interest for the following period is computed by using the new principal (original principal plus interest). In effect, the bank is computing interest on interest, which is called compound interest. Interest that is computed on the principal and any accumulated interest is called compound interest. Compound Interest Formula nt r A p 1 n Where, A is the amount, p is the principal, r is the annual rate of interest, t is the time in years, and n is the number of compounding periods per year. Present Value You may wonder about what amount of money you must deposit in an account today to have a certain amount of money in the future. The principal, p, which would have to be invested now, is called the present value. Present Value Formula A p nt r 1 n 11.4 Installment Buying There are two types of installment loans: open-end and fixed payment An open-ended installment loan is a loan on which you can make variable payments each month. An example of an open-ended installment loan is a credit card A fixed installment loan is one on which you pay a fixed amount of money for a set number of payments. An example is a car loan, boat loan, or a college tuition loan. Congress passed the Truth in Lending Act in 1969 which requires that the lending institution tell the borrower two things: the annual percentage rate (APR) and the finance charge. The APR is the true rate of interest charged for the loan The total finance charge is the total amount of money the borrower must pay for its use. The finance charge includes the interest plus any additional fees charged. Fixed Installment Loan Often times a person with an outstanding fixed loan opts to pay the loan off before the date of maturity. In this case the customer is not obligated to pay the entire finance charge. The amount of the reduction of the finance charge from paying off the loan early is called unearned interest. The most common way of calculating unearned interest is the actuarial method. Actuarial Method for Unearned Interest n P V u 100 V Where u is the unearned interest, n is the number of remaining monthly payments (excluding current payment), P is the monthly payment, and V is the value from the APR table that corresponds to the annual percentage rate for the number of remaining payments (excluding the current payment). Open-End Installment Loan Credit cards: For purchases there is no finance or interest charge if there is no previous balance due and you pay the entire new balance by the payment due date However, if you borrow money (cash advance) through this account, a finance charge is applied from the date you borrowed the money until the date you repay the money When you make purchases or borrow money, the minimum monthly payment is sometimes determined by dividing the balance due by 36 and rounding the answer up to the nearest whole dollar, thus ensuring repayment in 36 months. If the balance due for any month is less than $360, the minimum monthly payment is typically $10 These general guidelines may vary by bank. Calculating finance charges when there are no additional transactions in the account for the period When additional charges are made during the period, the finance charges can be calculated in two ways: One way is using the unpaid balance method. The borrower is charged interest or a finance charge on the unpaid balance from the previous charge period The second way is using the average daily balance method. Many lending institutions believe this method is fairer to the customer. With this method, a balance is determined each day of the billing period for which there is a transaction in the account. 11.5 Buying a House with a Mortgage A homeowner’s mortgage is a long-term loan in which the property is pledged as a security for payment of the difference between the down payment and the sale price. The down payment is the amount of cash the buyer must pay to the seller before the lending institution will grant the buyer a mortgage. The two most popular types of mortgage loans available today are the adjustable- rate loan and the conventional loan. The major difference between the two is that the interest rate for the conventional loan is fixed for the duration of the loan, whereas the interest for the adjustable- rate loan may change every period, as specified in the loan. The size of the down payment required depends on who is lending the money, how old the property is, and whether or not is it easy to borrow money at that particular time. Most lending institutions may require the buyer to pay one or more points for their loan at the time of closing (the final step in the sale process) One point amounts to 1% of the mortgage money (the amount being borrowed). By charging points, the bank reduces the rate of interest on the mortgage, thus reducing the size of the monthly payments and enabling more people to purchase houses. Banks use a formula to determine the maximum monthly payment that they believe is within the purchaser’s ability to pay. A mortgage loan officer first determines the buyer’s adjusted monthly income by subtracting from the gross monthly income (total income before any deductions) any fixed monthly payments with more than 10 months remaining (such as a student loan, a car, insurance, etc). The loan officer then multiplies the adjusted monthly income by 28%. In general, this product is the maximum monthly house payment the lending institution believes the purchaser can afford to pay. This payment must cover principal, interest, property taxes, and insurance.