Chapter 9: Consumer Mathematics Definition: Percent To convert a percent to a decimal, drop % and move the decimal two places left. Examples: To convert a percent to a fraction, drop %, use percent as numerator and 100 as denominator. Examples: To convert decimal to percent, move decimal place two places right and add percent sign. Examples: To change a fraction to a percent, change the fraction to a decimal and the decimal to a percent. Examples: Percent problems are of three types: finding a part, finding a percent, or finding a base. The relationship is Part = Rate Base Examples: 1
Example: A pair of jeans was originally $60 but marked down to $20. What was the percent reduction in price? Example: The local sales tax is 7%. How much tax will be paid on an item that costs $25? Section 9.2: Interest Definitions: Interest Principal Rate Term Maturity Value The simple interest formulas are: Interest=Principal Rate Time (or I = P RT ) 2
and Maturity Value = Principal +Interest (MV = P + I or MV = P (1 + RT )). Example: Find the interest on a loan of $5000 for 4 years at a rate of 5% per year. Example: Sam must borrow $1000 for 4 months at 2%. Find the interest she must pay. Example: If Sam wanted to make monthly payments, how much should she pay per month? 3
Example: Jan borrowed $4000 at 6% simple interest to buy a car. She paid $720 in interest. Find the term of the loan. Compound Interest Formulas: MV = P ( 1 + r ) nt n where n is the number of times compounded per year, r is the yearly interest rate, t is the term of the loan in years. Example: Find the interest on $4000 compounded semiannually at 4% for 6 years. Definition: The effective rate (annual yield) 4
Example: Find the effective rate of 4% compounded semiannually. Definition: An annuity is: Example: Find the future value of an annuity when the payment is $800 semiannually, interest rate is 5% compounded semiannually, and term is 4 years. Section 9.3: Installment Buying 5
The finance charge is the cost of borrowing money. There are two methods for computing a finance charge: 1. Unpaid balance 2. average daily balance In the unpaid balance method, interest is only charged on the balance from the previous month. Example: For the month of July, the unpaid balance on Sue s card was $1161.63 at the beginning of the billing cycle. She made purchases of $512.58 and made a payment of $250.00 during the month. If the interest rate is 1.75% per month on the unpaid balance, determine the finance charge and her new balance on August 1. In the average daily balance method, the balance on each day of the month is used to compute the average daily balance. The procedure is: 1. Find the balance for each transaction. 2. Find the number of days for each balance. 3. Multiply the balances by the number of days and find sum. 4. Divide sum by the number of days in the month. This is the average daily balance. 5. Find the finance charge on the average daily balance. 6. Find the new balance. Example: A credit card statement showed the following transactions: 6
3/1 previous balance 2162.56 3/3 payment 800 3/10 purchase 329.27 3/21 payment 500 3/29 purchase 197.26 1. Find the average daily balance. 2. Find the finance charge if the interest rate is 2% per month on the average daily balance. 3. Find the new balance on 4/1. The APR is the true rate of interest on a loan. We have AP R 2NI P (T + I) where N is the number of payments per year, I is the finance charge, P is the principal, and T is the total number of payments. Example: A store borrowed $300.00 to buy extra supplies in December. It is to be paid back in 18 monthly installments of $18.17. Find the APR. 7
Section 9.4: Home Ownership Definition: A mortgage is: To find the monthly payment for a fixed-rate mortgage: 1. find the down payment 2. subtract the down payment from the cost of the home. This is the principal. 3. Divide the principal by 1000. 4. Lookup appropriate value in the table in the text. 5. Multiply that value by result from (3) to get monthly payment. Example: A house sells for $82,500 and a 5% down payment is made. The mortgage is secured for 10% for 15 years. 1. Find the down payment. 2. Find the amount of the mortgage. 3. Find the monthly payment. 4. Find the total interest paid. 5. Find an amortization schedule for the first two payments. 8
For property tax, the millage rate is 1 1000 of $1. Example: A millage rate of 25 mills means a homeowner would pay $25 for each $1000 that a house is worth. Example: Find the property tax on a building whose market value is $127,000 assessed at 30% of market value. The tax rate is 85 mills. Section 9.5: Markup and Markdown Definition: Markup Note that M = S C, S = C + M, C = S M! Markup on Cost Example: A store sells jeans for 60% markup on cost. If the jeans cost the merchant $20, find the selling price. 9
Example: If an item costs $250.00 and sells for $400.00, find the markup rate. Markup on Selling Price Example: An item sells for $40 and is marked up 20% on selling price. Find the cost of the item. Example: The markup on the selling price of an item is $16. If the item sells for $25, find the markup rate. 10
and To convert between markup on cost and markup on selling price, use the following: markup on selling price = markup on cost = markup rate on cost 1 + markup rate on cost markup rate on selling price 1 markup rate on selling price Example: Find the markup on cost of the markup on selling price is 20%. Markdown: ALWAYS use selling price as the base! Example: An item sells for $25 and is marked down 15%. Find the reduced price. 11