Chapter 11 Note Packet 11.1 Percents

Transcription

1 Chapter 11 Note Packet Name: 11.1 Percents Example 1: A Yahoo! Question of the Week asked, "At what age do you consider someone old?" Out of the 3496 respondents, 1017 said that age 80 is old. What percent of respondents feel that age 80 is old? Example 2: According to the WHO on May 1, 2003, there were 5865 people worldwide with SARS. Of these cases 5238 were in China, 201 were in Singapore, and 279 were in Canada. Determine the percent of SARS cases that fell in the following countries: China, Singapore, Canada, Other. Example 3: In 2002 the MLB team with the most improved record was the Anahiem Angels. In 2001 the Angels won 75 games. In 2002 they won 99 games. Find the percent change. Example 4: In 1991, there were approximately 16,568,000 labor union members in the United States. By 2001 this number had dropped to 16,275,000. Find the percent change in union membership. Example 5: Holdren Hardware stores pay $18.76 for glass fireplace screens. They regularly sell them for $ At a sale they sell them for $ Find: a) the percent markup on the regular price. b) the percent markup on the sale price. c) the percent decrease of the sale price from the regular price. Example 6: Melissa Bell wishes to buy a house for $87,000. To obtain a mortgage, she needs to pay 20% of the selling price as a down payment. Determine the amount of Melissa's down payment.

2 Example 7: In 2002, about 50,000 out of the 88,000 US Chess Federation members competed in USCF tournaments. What percent of USCF members competed in USCF tournaments? Example 8: About 35,640,000, or 36% of Mexico's population is younger than 15 years old. What is the population of Mexico? 11.2 Personal Loans and Simple Interest CREDIT or PRINCIPAL OF THE LOAN SECURITY or COLLATERAL COSIGNERS PERSONAL NOTE INTEREST SIMPLE INTEREST ORDINARY INTEREST Example 1: Joe Johns needs to borrow $1600 to have corrective eye surgery. From her credit union, she obtains a 9-month loan with an annual simple interest rate of 6.5%. a) Calculate the simple interest on the loan. b) Calculate the amount that Joe will pay the credit union at the end of nine months. Example 2: Patricia Allen lent her friend Dan Marcus $300 to help him pay his income taxes. Six months later Dan repaid Patricia $315. What annual rate of interest did Patricia receive? Example 3: To obtain money for glasses, Gilbert pawns his trumpet. Gilbert borrows $240 and after 35 days he pays back $288. What annual rate of interest did Gilbert pay?

3 DISCOUNT NOTE BANK DISCOUNT Example 4: Jane Adams borrowed $5000 on a 10% discount note for a period of three months. Find: a) The interest she must pay to the bank on the date she receives the loan. b) The net amount of money she receives from the bank. c) The actual rate of interest for the loan. DATE OF ORIGINATION DATE OF MATURITY UNITED STATES RULE BANKERS RULE Example 5: Determine the due date of a loan made on March 15 for 120 days. Example 6: Determine the number of days from April 18 to July 31 Example 7: Determine the simple interest, using the Banker's Rule, that will be paid on a $300 loan at an interest rate of 5% for the period of March 3 to May 3.

4 Example 8: Cathy Johnson is a carpenter and plans to go to a conference. She takes out a $400 loan on November 1, 2002 for 120 days at a rate of 12.5%. Cathy uses birthday gift money to make a payment of $150 on January 3, She makes a second partial payment of $100 on February 2, a) What is the actual due date of the loan? b) What part of the January 3rd payment went towards interest? Principal? c) What is the remaining balance after January 3rd? d) What part of the February 2nd payment went towards interest? Principal? e) What is the remaining balance after February 2nd? f) What does Cathy owe on the date of maturity?

5 11.3 Compound Interest INVESTMENT FIXED INVESTMENT VARIABLE INVESTMENT EFFECTIVE ANNUAL YIELD or ANNUAL PERCENTAGE YIELD (APY) PRESENT VALUE Example 1: When Alexander was born, he received several gifts of cash from his relatives. His father invested this money in a money market account that had a rate of 3% compounded monthly. If the amount invested was $3200, determine the amount in the account after 5 years. Example 2: Calculate the interest on $650 at 8% compounded semiannually for 3 years. Example 3: Determine the APY for: a) 8% compounded daily. b) 6% compounded quarterly. Example 4: Nicholas is currently in the 8th grade and intends to attend a state university. If Nicholas needs $25,000 to pay for college how much do his parents have to invest now in a 48 month CD with a rate of 4.59%?

6 11.4 Installment Buying APR/Financing OPEN-END INSTALLMENT LOAN FIXED INSTALLMENT LOAN ANNUAL PERCENTAGE RATE (APR) FINANCE CHARGE TOTAL INSTALLMENT PRICE ACTUARIAL METHOD and RULE OF 78s UNEARNED INTEREST UNPAID BALANCE METHOD AVERAGE DAILY BALANCE METHOD Example 1: John wishes to buy a HDTV for $4500. The store is advertising a financing option of no down payment and 7% APR for 24 months. Determine the finance charge and monthly payment. Example 2: Al and Jill are purchasing a piano for $5000, including taxes. They decide to make a $1000 down payment and finance the balance. The loan states that the monthly payment is $121 per month for 36 months. Determine the finance charge and APR. Example 3: Tino borrowed $9800 to purchase a 65 Ford Mustang. If his payments are $237 for 48 months, what is the APR?

7 Example 4: If Tino decides to pay off his loan on the 30th payment, using the actuarial method how much interest will he save? What is the total amount due on the 30th payment to pay off the loan? Example 5: If Tino decides to pay off his loan on the 30th payment, using the rule of 78s method how much interest will he save? What is the total amount due on the 30th payment to pay off the loan? 11.4 Installment Buying Credit Cards Example 6: This month Jan charged $520 for Christmas gifts on her MasterCard which she had just paid off the month before. The bank requires repayment within 36 months and charges an interest rate of % per day on any unpaid balances from a previous billing cycle. a) What is the minimum payment on December 1? b) If Jan makes a payment of $100 on December 1, what is her balance due on January 1 assuming she makes no additional charges? Example 7: Ed charged the supplies for his Halloween party on his Visa which was previously paid off. On November 5, the billing date Ed Had a balance due of $275. From November 5 through December 4 he did some additional shopping totaling $320, and he also made a payment of $145. a) Find the finance charge due on December 5 if his interest rate is 1.3% per month. b) Find the new account balance as of December 5. c) Determine the minimum payment required as of December 5. Remember banks expect repayment within 36 months.

8 Example 8: The balance on Ming's credit card on July 1 was $ The following transactions occurred during July: July 5 Payment $ July 10 Charge $74.35 July 18 Charge $ July 20 Payment $ July 28 Charge $42.50 Find the following: a) Average daily balance b) Finance charge to be paid on August 1 given 3.8% interest per month. c) The balance due on August 1.

9 Mortgages DOWN PAYMENT HOMEOWNER'S MORTGAGE ADJUSTABLE-RATE or VARIABLE-RATE LOAN CONVENTIONAL LOAN POINTS ADD ON RATE or MARGIN PERIODIC RATE CAP AGGREGATE RATE CAP PAYMENT CAP CLOSING ADJUSTED MONTHLY INCOME Example 1: Chris and Daryl Cahill want to purchase a home selling for $125,000. Their bank requires a 15% down payment and a payment of 1 point at the time of closing. a) What is the amount of the down payment required? b) What is the mortgage amount? c) What is the cost of one point to be paid for by the Chaill's? Example 2: Suppose the Cahill's gross monthly income is $4200 and that they have 15 payments of $185 per month remaining on their car loan and 14 remaining payments of $35 per month on a loan used too purchase a new washer and dryer. The taxes on the house they want to purchase are $135 per month and the insurance is $38 per month. a) What is the maximum monthly payment that the Cahill's can afford according to the bank? b)the Cahill's want a 30 year fixed mortgage. If the bank is currently offering a 6.5% interest rate determine whether the Cahill's qualify for the mortgage.

10 Example 3: The Cahills obtained a house selling for $125,000. They made a 15% down payment and obtained a 30-year conventional mortgage for $106,250 at 6.5%. They also paid 1 point at closing. Their monthly mortgage payment of principal and interest is $ a) Determine the total amount of principal, interest, down payment, and points that the Cahills will pay the bank for their house over 30 years. b) How much of the cost will be interest? c) How much of the first payment on the mortgage is applied to the principal? Example 4: Tony and Keisha purchased a house for $1,150,000 with a down payment of $23,100. They obtained a 30-year adjustable rate mortgage with the following terms: The interest rate is based on a 6-month Treasury bill. The interest rate is 3% above the interest rate of the 6-month bill. The interest rate is adjusted every 6 months on the date of adjustment. The interest rate will not change more than 1% when the rate is adjusted. The maximum interest rate for the duration of the loan is 12% There is no lower limit on the interest rate. The initial mortgage interest rate is 5.5% and the monthly payments are adjusted every 5 years. a) Determine the initial monthly payment. b) Determine the adjusted interest rate in 6 months if the interest rate on the Treasury bill at that time is 2%