Chapter 3: Credit Cards and Consumer Loans

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Chapter 3: Credit Cards and Consumer Loans"

Transcription

1 Chapter 3: Credit Cards and Consumer Loans In these tough economic times, credit card debt has escalated to a new high. Lenders like American Express, Citigroup, Discover, Capital One etc. are tightening their standards thereby making it more difficult to get a new credit card and they are also cutting credit limits. Here, we will learn how mathematics is used in credit cards and how to use credit cards wisely. Mostly we use a credit card to make a large purchase. When we use a credit card, we are actually receiving loan which we have to eventually pay back. Generally, this loan payment is done in installments. There are two types of loans used for installment purchases: Closed-End Credit and Open-End Credit. A. Closed-End Credit This is the first type of consumer credit installment plan. Closed-End Credit is a loan where you make equal payments at regular intervals for some specific period of time. It is also called an installment loan. It is a traditional way of paying off loans. Mostly these loan payments are made monthly. An installment is the name given to each of these loan payments. The size of the payment is determined by the amount of the purchase and also the interest rate charged on the loan. The interest charged on the loan is called the finance charge. Method to compute the payments on an installment loan: Add-On Interest Method In this method, we use the simple interest formula to calculate the finance charge on the loan. Then the interest is added to the amount borrowed so that both the interest and the amount borrowed are paid back over the time period for which the loan was taken. The formula for the payment (installment) is given by P I Installment n where P = loan amount (present value), n = total number of payments I = amount of interest due on the loan (finance charge), 1

2 Example 1 Suppose that you take an add-on loan for $1000 to buy a washer/dryer at an annual rate of interest of 10% to be repaid in monthly installments over four years. How much will your monthly payments be? Solution: P = 1000, n = 4 x 12 = 48 months We calculate the interest using the simple interest formula: I = Prt = 1000 x.1 x 4 = $ 400. Thus, the monthly payment is = Example $ Suppose that you take an add-on loan for $28,000 at an annual rate of interest of 3.5% to be repaid in yearly installments over thirty years. How much will be your yearly payments? Solution: P = 28000, n = 30 years We calculate the interest using the simple interest formula: I = Prt = x.035 x 30 = $ Thus, the yearly payment is = Example $ Suppose that you take an add-on loan for $4,000 at an annual rate of interest of 5.45% to be repaid in semi-annual (six-month) installments over two years. How much will your semi-annual payments be? Solution: P = 4000, n = 4 semi-annual installments We calculate the interest using the simple interest formula: I = Prt = 4000 x.0545 x 2 = $ 436. Thus, the semi-annual payment is = $

3 Annual Percentage Rate (APR): In the add-on interest method you are not keeping the entire borrowed amount for the entire time of the loan period, which makes us wonder if the annual interest rate told to us is actually correct. Let us take a simple example to understand what a true APR is. Suppose you borrow $3000 to be repaid in three yearly installments using an add-on interest rate of 10%. What is your true interest rate? Using the add-on method, we can find the amount of interest by using the formula I = Prt = 3000 x.10 x 3 = $ 900. Thus, the amount to be paid back in three yearly installments is = $3900. Therefore, each payment is 3900 / 3 = $ 1300, of which 1000 is being paid on the principal and $300 is for the interest. Hence, for the first year you borrowed $ 3000 and paid an interest of $ 300. Then using the simple interest formula, the interest rate was 10% ( 300 = 3000 x r x 1), which is the same as the annual interest rate. Now in the second year, you make a payment of $1300, of which $ 1000 goes to reduce the principal and $ 300 is interest. Keep in mind that you have already paid back $1000 of the loan. Thus, you now have only $2000 to pay back and so you have paid $300 interest on a $2000 loan. Let us calculate the interest rate we have paid in the second year. Use simple interest formula: 300 = 2000 x r x 1. We find interest rate to be r =.15 or 15%. So in reality the interest rate on the loan for the second year is 15%. Now in the third year, you make the final payment of $1300. For this last year, you have paid $300 interest on a $1000 loan. Let us calculate the interest rate we have paid in the third year. Use simple interest formula: 300 = 1000 x r x 1. We find interest rate to be r =.3 or 30%!. So in reality the interest rate on the loan for the third year is 30%. Question: What is the true interest rate for this loan? The true interest rate we are looking for is called the Annual Percentage Rate. We will denote it by a. We see that the Interest for the first year + interest for the second year + interest for the third year = 900 Using the simple interest formula we can write this as 3000 x a x x a x x a x 1 = a = 900 a = 900 / 6000 =.15 Thus, the annual percentage rate is 15%. 3

4 Formula to approximate the Annual Percentage Rate for an add-on interest loan is 2nr APR n 1 Where r annual interest rate, n total number of payments. In 1968, the Truth-in Lending Act was passed by the Congress. This act requires all lenders to state the true annual interest rate, which is called the APR and is based on the actual amount owed. This regulation enables you to compare interest rates before you sign a contract, which must state the APR even if you haven t asked for it. Example 4: Consider a 2007 Blazer with a price of $28,505 that is advertised at a monthly payment of $631 for 60 months. What is the APR (to the nearest tenth of a percent)? We know A = P + I; I = 631(60) = Then we use the simple interest formula ( I = Prt) to find r: r = I / Pt = 9355 / ( 5) =.0656 ( Note that 60 months = 5 years) 2nr 2(60)(.0656) APR % n 1 61 Example 5: Sara purchases a sofa set for a price of $2500 with a loan that advertises a 9% simple interest rate to be repaid in three equal monthly payments. What is the APR (to the nearest tenth of a percent)? 2nr APR n 1 2(3)(.09) % 4

5 Problems: 1. Use the add-on method for determining the installments for the following. The amount of the loan, the annual interest rate, the term of the loan is given, and the installment plan. a. $879, 12%, 2 years, monthly b. $ 6390, 7.80%, 5 years, monthly c. $900, 10%, 6 years, semi-annually d. $ 790, 5.40%, 3 years, every six months e. $1320, 13.5%, 6 months, every two months f. $7890, 6.5%, 60 months, yearly g. $ 800, 12.77%, 3 years, monthly h. $ 5400, 11.05%, 8 years, quarterly i. $ 600, 4.5%, 2 years, quarterly 2. Find the APR on the add-on loan amount using the given number of payments and annual interest rate. a. n = 36, r = 6.4% b. n = 48, r = 4.8% c. n = 42, r = 7% d. n = 30, r = % 3. Ann took out a 24-month add-on loan for the amount $2000 to go to China at an interest rate of 8%. What is her APR (round to the nearest tenth)? 4. What is the APR of a 36-month add-on loan with an interest rate of 8.2%? 5. Trey took out a $25, 000 loans to remodel his house and will repay it by making 60 monthly payments of $485. Find his APR on the remodeling loan. 6. Carrie took an add-on loan for $1500 to buy a new laptop and will repay it by making 24 monthly payments of $ What is Carrie s APR on the loan? 5

6 7. Decide which has better APR if you want to repay a $ 5000 loan. Assume that you are making monthly payments. a. An add-on interest loan at 8.4% for 3 years b. 24 payments of $ 230 ( hint: You have to find the interest rate first.) 8. Decide which has better APR if you want to repay a $ 5000 loan. Assume that you are making monthly payments. a. An add-on interest loan at 8.4% for 1 years b. 24 payments of $ 240 ( hint: You have to find the interest rate first.) 9. Decide which has better APR if you want to repay a $ 5000 loan. Assume that you are making monthly payments. a. An add-on interest loan at 7.2% for 2 years b. 36 payments of $ 165 ( hint: You have to find the interest rate first.) 10. Jamie is buying a new boat for $ 11,000. The dealer is charging him an annual interest rate of 9.2% and is using the add-on method to compute his monthly payments. If Jamie pays off the boat in 48 months. a. What are his monthly payments? b. If he makes a down payment of $2000, how much will be his monthly payments? c. Estimate the APR. 11. Kelly buys a computer for $2400. If Kelly agrees to repay the balance in 24 equally monthly payments at an annual simple interest rate of 10%. a. What are her monthly payments? b. If she makes a down payment of $360, how much will be her monthly payments? c. Estimate the APR. 6

7 B. Open-End Credit This is a second type of consumer credit. It is also called revolving credit or a credit card loan. Examples of this type of credit card loan are MasterCard, American Express, Discover etc. This type of loan allows for purchases or cash advances up to a specified maximum line of credit and has a flexible repayment schedule. There are several ways a credit card company charges finance charges. We will look at two methods. I. Unpaid Balance Method In the Unpaid Balance Method, the finance charges are applied on the previous month s balance. Most of the credit cards issue monthly bills. The due date on the bill is usually 1 month after the billing date (the date the bill is prepared and sent to the customer). If you pay the bill by the due date, then no finance charges are applied; otherwise a finance charge is added to the next bill. This method uses the simple interest formula to calculate the finance charge on the balances you owe to the credit card company. The formula for the amount P you will owe is P = previous month s balance + finance charge + purchases made payments returns Example 6 Suppose you have a credit card which has an annual rate of interest of 18% and at the beginning of the last month you had an unpaid balance of $144. Since then you returned the winter boots you had bought for $75.00, made a purchase of a dell desktop for $500, and sent in a payment of $200. What is the balance you owe for this month? What is your finance charge for the next month? Solution: First we will calculate the finance charge on previous month balance: I = 144 x.18 x ( ) = $ 2.16 Now we will find the balance you owe the credit card company for this month. P = = $ To find the finance charge for the next month we apply the simple interest formula on the new amount ($ ) which you owe for this month: I = Prt = x.18 x ( ) = $ It is easy to use to credit cards for purchases and to only pay the minimum payment stated on the credit card bill. This is dangerous as it will lead to an increase in what you owe and sometimes it gets out of hand. Let us look at an example. 7

8 Example 8 Suppose Tom has a credit card debt of $ 4000 which has an annual rate of interest 18%. The minimum payment for the month of June is $60. Suppose Tom pays back only the minimum required payment. What is the balance Tom has to pay back at the end of June? The finance charges are computed using the unpaid balance method. Solution: Tom s interest is I = Prt = (4000)(.18)(1/12) = $60. Thus at the end of June he will owe P = = $4000! Tom has made no progress in paying down his credit card debt! 8

9 Problems: 1. Given last month s balance, the annual interest rates, and any other transactions, find the amount you owe and the finance charge to be paid on this month s credit card, using the unpaid balance method. a. Last month balance $ 5000; rate 21%; returned TV $1000, payment $600 b. Last month balance $ 800; rate 16%; bought sandals $100, payment $300 c. Last month balance $ 500; rate 19%; bought calculator $82, returned jeans $30.00, payment $180 d. Last month balance $ 1300; rate 20%; bought socks $10, bought iron $30, returned lamp $45.00, returned luggage $145.00, payment $ Tracy bought personal computer for $ using her credit card which has 18% annual interest rate. The unpaid balance on her credit card at the beginning of last month was $ 300. Since then, she has purchased her statistics book for $ and sent in payment of $ 200. Using the Unpaid balance method, what is her credit card bill this month? What is her finance charge next month? 3. Compute the finance charge for the Month of August ( 31 days), when the previous month s (July) balance was $ 280 and the following transaction took place in the month of August. Assume an annual interest rate of 21%. Date Transaction August 5 Made payment of $75 August 10 Charged $ 130 for trekking boots August 18 Charged $ 40 for gas August 23 Charged $30.34 for restaurant meal 4. Compute the finance charge for the Month of November ( 30 days), when the previous month s balance was $ 212 and the following transaction took place in the month of November. Assume an annual interest rate of 21%. Date Nov. 9 Transaction Charged $ 40 for DVD Nov. 15 Charged $ 34 for gas Nov. 21 Made payment of $175 Nov. 23 Charged $ for groceries 9

10 II. Average Daily Balance Method In reality, many credit card companies use the average daily balance method to calculate the interest on the balance you have. In this method, the finance charge is based on the balance in the account for each day of the billing period. It is calculated by dividing the sum of the total amounts owed each day by the number of days in the billing period. Example 8: sum of the total amounts owed each day Average Daily Balance number of days in the billing period Suppose an unpaid bill of $315 had a due date of April 10. A purchase of $28 was made on April 12, and $123 was charged on April 24. A payment of $50 was made on April 15. The next billing date is May 10. The interest on the average daily balance is 18%. Find the finance charge on the May 10 bill. Solution: First we will create a table showing the unpaid balance for each purchase, the number of days the balance is owed, and the product of these numbers. A negative sign in the payments or purchases column of the table indicates that a payment was made. Date Payments or Purchases Balance each Day No. of days until Balance Changes Unpaid Balance Times Number of Days April $ $ 630 April $ 28 $ $ 1029 April $ 50 $ $ 2637 April 24-May 9 $ 123 $ $ 6656 Total $ 10,952 10,952 Average daily balance = $ The finance charge is given by I = Prt = (.18)(30/365) $

11 Problems: 1. Calculate the finance charge for a credit card that has given average daily balance and interest rate. Assume a 30 day billing period. a. Average daily balance = $ ; annual interest rate = 15% b. Average daily balance = $ ; annual interest rate = 21% c. Average daily balance = $ ; annual interest rate = 18% d. Average daily balance = $ ; annual interest rate = 21% 2. Use the average daily balance method to compute the finance charge on the credit card account for the stated month. The starting balance and transactions on the account for the month are given. Assume an annual interest rate of 21%. a. Compute the finance charge for the month of August (31 days), when the previous month s (July) balance was $280 and the following transaction took place in the month of August. Date Transaction August 5 Made payment of $75 August 10 Charged $130 for trekking boots August 18 Charged $40 for gas August 23 Charged $30.34 for restaurant meal b. Compute the finance charge for the month of November (30 days), when the previous month s balance was $212 and the following transaction took place in the month of November. Date Nov. 9 Transaction Charged $40 for DVD Nov. 15 Charged $34 for gas Nov. 21 Made payment of $175 Nov. 23 Charged $ for groceries 3. A credit card account had a $244 balance on March 5. A purchase of $152 was made on March 12, and a payment of $100 was made on March 28. Find the average daily balance and the finance charge if the billing date is April 5. Assume an annual interest rate of 21%. 11

If P = principal, r = annual interest rate, and t = time (in years), then the simple interest I is given by I = P rt.

If P = principal, r = annual interest rate, and t = time (in years), then the simple interest I is given by I = P rt. 13 Consumer Mathematics 13.1 The Time Value of Money Start with some Definitions: Definition 1. The amount of a loan or a deposit is called the principal. Definition 2. The amount a loan or a deposit increases

More information

MTH 150 SURVEY OF MATHEMATICS. Chapter 11 CONSUMER MATHEMATICS

MTH 150 SURVEY OF MATHEMATICS. Chapter 11 CONSUMER MATHEMATICS Your name: Your section: MTH 150 SURVEY OF MATHEMATICS Chapter 11 CONSUMER MATHEMATICS 11.1 Percent 11.2 Personal Loans and Simple Interest 11.3 Personal Loans and Compound Interest 11.4 Installment Buying

More information

Compound Interest Formula

Compound Interest Formula Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the present value for the given future amount. Round to the nearest cent. 1) A = $4900,

More information

Math 1332 Test 5 Review

Math 1332 Test 5 Review Name Find the simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month. 1) $1660 at 6% for 4 months Find the future value of the deposit if the

More information

9.3. Consumer Loans Objectives

9.3. Consumer Loans Objectives 9.3 Consumer Loans Objectives 1. Determine payments for an add-on loan. 2. Compute finance charges on a credit card using the unpaid balance method. 3. Use the average daily balance method to compute credit

More information

11.4 Installment Buying

11.4 Installment Buying 11.4 Installment Buying Open-end installment loan: a loan on which you can make variable payments each month, e.g. credit cards Fixed installment loan: a loan on which you pay a fixed amount of money for

More information

Section 8.1. I. Percent per hundred

Section 8.1. I. Percent per hundred 1 Section 8.1 I. Percent per hundred a. Fractions to Percents: 1. Write the fraction as an improper fraction 2. Divide the numerator by the denominator 3. Multiply by 100 (Move the decimal two times Right)

More information

Amortized Loan Example

Amortized Loan Example Amortized Loan Example Chris Columbus bought a house for $293,000. He put 20% down and obtained a 3 simple interest amortized loan for the balance at 5 % annually interest for 30 8 years. a. Find the amount

More information

Simple Interest. and Simple Discount

Simple Interest. and Simple Discount CHAPTER 1 Simple Interest and Simple Discount Learning Objectives Money is invested or borrowed in thousands of transactions every day. When an investment is cashed in or when borrowed money is repaid,

More information

Lesson 12 Take Control of Debt: Not All Loans Are the Same

Lesson 12 Take Control of Debt: Not All Loans Are the Same Lesson 12 Take Control of Debt: Not All Loans Are the Same Lesson Description This lesson examines the features of a loan with a fixed period of repayment (term loan). After distinguishing these loans

More information

Check off these skills when you feel that you have mastered them.

Check off these skills when you feel that you have mastered them. Chapter Objectives Check off these skills when you feel that you have mastered them. Know the basic loan terms principal and interest. Be able to solve the simple interest formula to find the amount of

More information

Ch. 11.2: Installment Buying

Ch. 11.2: Installment Buying Ch. 11.2: Installment Buying When people take out a loan to make a big purchase, they don t often pay it back all at once in one lump-sum. Instead, they usually pay it back back gradually over time, in

More information

Remember the Interest

Remember the Interest STUDENT MODULE 7.1 BORROWING MONEY PAGE 1 Standard 7: The student will identify the procedures and analyze the responsibilities of borrowing money. Remember the Interest Mom, it is not fair. If Bill can

More information

LINX EDUCATIONAL INSTRUCTOR S GUIDE

LINX EDUCATIONAL INSTRUCTOR S GUIDE EXTRA CREDIT: UNDERSTANDING THE DO S & DON TS OF USING CREDIT TAKING CHARGE OF CREDIT: 10 TIPS TO CREDIT DISCIPLINE Use the following suggestions as guidelines to self-discipline to keep your credit in

More information

Finance 197. Simple One-time Interest

Finance 197. Simple One-time Interest Finance 197 Finance We have to work with money every day. While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for

More information

Chapter F: Finance. Section F.1-F.4

Chapter F: Finance. Section F.1-F.4 Chapter F: Finance Section F.1-F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given

More information

Lesson 13 Take Control of Debt: Become a Savvy Borrower

Lesson 13 Take Control of Debt: Become a Savvy Borrower Lesson 13 Take Control of Debt: Become a Savvy Borrower Lesson Description After reviewing the difference between term loans and revolving credit, students analyze a fictitious character s use of credit

More information

Credit Card Loans. Student Worksheet

Credit Card Loans. Student Worksheet Student Worksheet Credit Card Loans Name: Recall the formula for simple interest where, I is the interest owed P is the principal amount outstanding r is the interest rate t is the time in years. Note:

More information

Warm-up: Compound vs. Annuity!

Warm-up: Compound vs. Annuity! Warm-up: Compound vs. Annuity! 1) How much will you have after 5 years if you deposit $500 twice a year into an account yielding 3% compounded semiannually? 2) How much money is in the bank after 3 years

More information

Present Value (PV) Tutorial

Present Value (PV) Tutorial EYK 15-1 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,

More information

Finite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan

Finite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan Finite Mathematics Helene Payne CHAPTER 6 Finance 6.1. Interest savings account bond mortgage loan auto loan Lender Borrower Interest: Fee charged by the lender to the borrower. Principal or Present Value:

More information

C:\Documents and Settings\tracey_hbutters\Desktop\mathematics\year_levels\math_stage6\General\hsc\financial_maths\financial5\annuities_loan_repa

C:\Documents and Settings\tracey_hbutters\Desktop\mathematics\year_levels\math_stage6\General\hsc\financial_maths\financial5\annuities_loan_repa Annuities and Loan Repayments H General Maths HSC NAME: 1 HSC CAPACITY MATRIX GENERAL MATHEMATICS TOPIC: Financial Mathematics 5 Annuities & loan repayments 3 weeks AM1 rn1 CONTENT CAPACITY BREAKDOWN!

More information

Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization

Finance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need

More information

300 Chapter 5 Finance

300 Chapter 5 Finance 300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for $200,000 with a down payment of $40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which

More information

How To Cut The Cost of Credit

How To Cut The Cost of Credit Published by the NATIONAL ASSOCIATION OF CONSUMER CREDIT ADMINISTRATORS May be reproduced with appropriate credit. For more information, contact: [ ] How To Cut The Cost of Credit Distributed by: Missouri

More information

Chapter 22: Borrowings Models

Chapter 22: Borrowings Models October 21, 2013 Last Time The Consumer Price Index Real Growth The Consumer Price index The official measure of inflation is the Consumer Price Index (CPI) which is the determined by the Bureau of Labor

More information

Calculating interest rates

Calculating interest rates Calculating interest rates A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Annual percentage rate 3. Effective annual rate 1. Introduction The basis of the time value of money

More information

Dr. Debra Sherrill Central Piedmont Community College

Dr. Debra Sherrill Central Piedmont Community College Dr. Debra Sherrill Central Piedmont Community College 2 Understand the types of installment loans. Identify ways to pay for college. Know how to purchase a car. 3 I. Introduction to Financial Terms II.

More information

The following is an article from a Marlboro, Massachusetts newspaper.

The following is an article from a Marlboro, Massachusetts newspaper. 319 CHAPTER 4 Personal Finance The following is an article from a Marlboro, Massachusetts newspaper. NEWSPAPER ARTICLE 4.1: LET S TEACH FINANCIAL LITERACY STEPHEN LEDUC WED JAN 16, 2008 Boston - Last week

More information

ISE 2014 Chapter 3 Section 3.11 Deferred Annuities

ISE 2014 Chapter 3 Section 3.11 Deferred Annuities ISE 2014 Chapter 3 Section 3.11 Deferred Annuities If we are looking for a present (future) equivalent sum at time other than one period prior to the first cash flow in the series (coincident with the

More information

Standard 7: The student will identify the procedures and analyze the responsibilities of borrowing money.

Standard 7: The student will identify the procedures and analyze the responsibilities of borrowing money. TEACHER GUIDE 7.2 BORROWING MONEY PAGE 1 Standard 7: The student will identify the procedures and analyze the responsibilities of borrowing money. It Is In Your Interest Priority Academic Student Skills

More information

MGF 1107 Spring 11 Ref: 606977 Review for Exam 2. Write as a percent. 1) 3.1 1) Write as a decimal. 4) 60% 4) 5) 0.085% 5)

MGF 1107 Spring 11 Ref: 606977 Review for Exam 2. Write as a percent. 1) 3.1 1) Write as a decimal. 4) 60% 4) 5) 0.085% 5) MGF 1107 Spring 11 Ref: 606977 Review for Exam 2 Mr. Guillen Exam 2 will be on 03/02/11 and covers the following sections: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6. Write as a percent. 1) 3.1 1) 2) 1 8 2) 3) 7 4 3)

More information

Chapter 2 Finance Matters

Chapter 2 Finance Matters Chapter 2 Finance Matters Chapter 2 Finance Matters 2.1 Pe r c e n t s 2.2 Simple and Compound Interest 2.3 Credit Cards 2.4 Annuities and Loans Chapter Summary Chapter Review Chapter Test Handling personal

More information

LESSON 10 CONSUMER CREDIT: BUY NOW, PAY LATER, AND MORE

LESSON 10 CONSUMER CREDIT: BUY NOW, PAY LATER, AND MORE LESSON 10 CONSUMER CREDIT: BUY NOW, PAY LATER, AND MORE INTRODUCTION The word credit comes from the Latin word creditus meaning entrusted. Credit means that someone will lend you money and give you time

More information

TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest!

TIME VALUE OF MONEY. Return of vs. Return on Investment: We EXPECT to get more than we invest! TIME VALUE OF MONEY Return of vs. Return on Investment: We EXPECT to get more than we invest! Invest $1,000 it becomes $1,050 $1,000 return of $50 return on Factors to consider when assessing Return on

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective

More information

$496. 80. Example If you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months?

$496. 80. Example If you can earn 6% interest, what lump sum must be deposited now so that its value will be $3500 after 9 months? Simple Interest, Compound Interest, and Effective Yield Simple Interest The formula that gives the amount of simple interest (also known as add-on interest) owed on a Principal P (also known as present

More information

Solutions to Time value of money practice problems

Solutions to Time value of money practice problems Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,

More information

LESSON SUMMARY. Mathematics for Buying, Selling, Borrowing and Investing

LESSON SUMMARY. Mathematics for Buying, Selling, Borrowing and Investing LESSON SUMMARY CXC CSEC MATHEMATICS UNIT Four: Consumer Arithmetic Lesson 5 Mathematics for Buying, Selling, Borrowing and Investing Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume

More information

Problem Set: Annuities and Perpetuities (Solutions Below)

Problem Set: Annuities and Perpetuities (Solutions Below) Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years

More information

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26 Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.

More information

The Basics of Interest Theory

The Basics of Interest Theory Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest

More information

For more information on plain English go to www.simplyput.ie. Transactions Involving Directors - A Quick Guide

For more information on plain English go to www.simplyput.ie. Transactions Involving Directors - A Quick Guide For more information on plain English go to www.simplyput.ie Transactions Involving Directors - A Quick Guide Transactions Involving Directors A Quick Guide Contents About this booklet 2 Who do the rules

More information

Average college senior has $2,800 in credit card debt

Average college senior has $2,800 in credit card debt Average college senior has $2,800 in credit card debt Even assuming no more new debt, if you make the minimum monthly payment, it will take about 30 years to pay it all off Credit and Credit Cards The

More information

21.1 Arithmetic Growth and Simple Interest

21.1 Arithmetic Growth and Simple Interest 21.1 Arithmetic Growth and Simple Interest When you open a savings account, your primary concerns are the safety and growth of your savings. Suppose you deposit $1000 in an account that pays interest at

More information

Annuities and Sinking Funds

Annuities and Sinking Funds Annuities and Sinking Funds Sinking Fund A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of compounded

More information

Loan Lessons. The Low-Down on Loans, Interest and Keeping Your Head Above Water. Course Objectives Learn About:

Loan Lessons. The Low-Down on Loans, Interest and Keeping Your Head Above Water. Course Objectives Learn About: usbank.com/student financialgenius.usbank.com Course Objectives Learn About: Different Types of Loans How to Qualify for a Loan Different Types of Interest Loan Lessons The Low-Down on Loans, Interest

More information

Handbook: The Cost of Borrowing. Learn what you need to know quickly.

Handbook: The Cost of Borrowing. Learn what you need to know quickly. Handbook: The Cost of Borrowing Learn what you need to know quickly. Money Matters Handbook: The Cost of Borrowing Groceries cost. Clothes cost. Furniture costs. And it costs to borrow money. The amount

More information

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

More information

Finance. Simple Interest Formula: I = P rt where I is the interest, P is the principal, r is the rate, and t is the time in years.

Finance. Simple Interest Formula: I = P rt where I is the interest, P is the principal, r is the rate, and t is the time in years. MAT 142 College Mathematics Finance Module #FM Terri L. Miller & Elizabeth E. K. Jones revised December 16, 2010 1. Simple Interest Interest is the money earned profit) on a savings account or investment.

More information

CALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time

CALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses

More information

Loan Lessons. The Low-Down on Loans, Interest and Keeping Your Head Above Water. Course Objectives Learn About:

Loan Lessons. The Low-Down on Loans, Interest and Keeping Your Head Above Water. Course Objectives Learn About: Loan Lessons Course Objectives Learn About: Different Types of Loans How to Qualify for a Loan Different Types of Interest The Low-Down on Loans, Interest and Keeping Your Head Above Water usbank.com/financialeducation

More information

Credit and borrowing. In this chapter. syllabusreference. Financial mathematics 4 Credit and borrowing

Credit and borrowing. In this chapter. syllabusreference. Financial mathematics 4 Credit and borrowing Credit and borrowing syllabusreference Financial mathematics 4 Credit and borrowing In this chapter A B C D E Flat rate interest Home loans The cost of a loan Credit cards Loan repayments reyou READY?

More information

5.1 Simple and Compound Interest

5.1 Simple and Compound Interest 5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?

More information

REPAYING YOUR LOAN EARLY. www.fla.org.uk

REPAYING YOUR LOAN EARLY. www.fla.org.uk REPAYING YOUR LOAN EARLY www.fla.org.uk REPAYING YOUR LOAN EARLY What this leaflet tells you Early repayment, or early settlement, is where you repay some or all of your loan before you were required to.

More information

Present Value Concepts

Present Value Concepts Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts

More information

Home Equity Loans and Lines of Credit

Home Equity Loans and Lines of Credit Delaware County Bank P.O. Box 1001 Lewis Center, OH 43035 740-657-7000 inforequest@dcb-t.com Home Equity Loans and Lines of Credit Page 1 of 5, see disclaimer on final page Home Equity Loans and Lines

More information

Financial Literacy. Credit basics

Financial Literacy. Credit basics Literacy Credit basics 2 Contents HANDOUT 6-1 Types of credit Type of credit Lender Uses Conditions Revolving credit Credit Cards (secured and unsecured NOT prepaid) To make purchases, pay bills, make

More information

Ch 3 Understanding money management

Ch 3 Understanding money management Ch 3 Understanding money management 1. nominal & effective interest rates 2. equivalence calculations using effective interest rates 3. debt management If payments occur more frequently than annual, how

More information

Advantages and Disadvantages of Using Credit

Advantages and Disadvantages of Using Credit 1 Lesson 7: About Credit Why Get Credit? To establish a credit history. Advantages and Disadvantages of Using Credit 1. Advantages Able to buy needed items now. Don t have to carry cash. Creates a record

More information

2.1 The Present Value of an Annuity

2.1 The Present Value of an Annuity 2.1 The Present Value of an Annuity One example of a fixed annuity is an agreement to pay someone a fixed amount x for N periods (commonly months or years), e.g. a fixed pension It is assumed that the

More information

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.

2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved. 2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical defined-contribution

More information

Case Study More Money Please

Case Study More Money Please Case Study More Money Please Question Appeared in: ModelOff 2015 Round 2 Time allocated: 35 minutes INTRODUCTION You work for a Project Company that has an existing senior debt facility which is due to

More information

E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is

E INV 1 AM 11 Name: INTEREST. There are two types of Interest : and. The formula is. I is. P is. r is. t is E INV 1 AM 11 Name: INTEREST There are two types of Interest : and. SIMPLE INTEREST The formula is I is P is r is t is NOTE: For 8% use r =, for 12% use r =, for 2.5% use r = NOTE: For 6 months use t =

More information

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value. Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

More information

ESSENTIAL QUESTION How do you calculate the cost of repaying a loan?

ESSENTIAL QUESTION How do you calculate the cost of repaying a loan? ? LESSON 16.1 Repaying Loans ESSENTIAL QUESTION How do you calculate the cost of repaying a loan? financial literacy 8.12.A Solve real-world problems comparing how interest rate and loan length affect

More information

Chapter 11 Note Packet 11.1 Percents

Chapter 11 Note Packet 11.1 Percents 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

More information

Chapter 6 Applications for Business and Consumers

Chapter 6 Applications for Business and Consumers Chapter 6 Applications for Business and Consumers Find the unit cost. Round to the nearest tenth of a cent. Grape juice, 64 ounces for $78 Black pepper, 2 ounces for $0.63 Peanut butter, 28 ounces for

More information

The Institute of Chartered Accountants of India

The Institute of Chartered Accountants of India CHAPTER 4 SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY APPLICATIONS SIMPLE AND COMPOUND INTEREST INCLUDING ANNUITY- APPLICATIONS LEARNING OBJECTIVES After studying this chapter students will be able

More information

Slide 11-1. Copyright 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION. Chapter 11. Consumer Mathematics 11.1.

Slide 11-1. Copyright 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION. Chapter 11. Consumer Mathematics 11.1. SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 11-1 Chapter 11 Consumer Mathematics 11.1 Percent 1 Percent The word percent comes from the Latin per centum, meaning per hundred. A percent is simply

More information

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION

CHAPTER 4 DISCOUNTED CASH FLOW VALUATION CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value

More information

"Get Your Money Straight!" EOP Workshop on Financial Literacy Fall 2008

Get Your Money Straight! EOP Workshop on Financial Literacy Fall 2008 "Get Your Money Straight!" EOP Workshop on Financial Literacy Fall 2008 Financial Literacy: Financial Aid and Student Loans Credit Budgeting Financial Aid Loan Repayment: Loan repayment begins 6 months

More information

Foundation review. Introduction. Learning objectives

Foundation review. Introduction. Learning objectives Foundation review: Introduction Foundation review Introduction Throughout FN1, you will be expected to apply techniques and concepts that you learned in prerequisite courses. The purpose of this foundation

More information

FINA 351 Managerial Finance, Ch.4-5, Time-Value-of-Money (TVM), Notes

FINA 351 Managerial Finance, Ch.4-5, Time-Value-of-Money (TVM), Notes FINA 351 Managerial Finance, Ch.4-5, Time-Value-of-Money (TVM), Notes The concept of time-value-of-money is important to know, not only for this class, but for your own financial planning. It is a critical

More information

DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one

More information

CHAPTER 1. Compound Interest

CHAPTER 1. Compound Interest CHAPTER 1 Compound Interest 1. Compound Interest The simplest example of interest is a loan agreement two children might make: I will lend you a dollar, but every day you keep it, you owe me one more penny.

More information

BORROWING MONEY FOR YOUR BUSINESS

BORROWING MONEY FOR YOUR BUSINESS BORROWING MONEY FOR YOUR BUSINESS Disclaimer: There are thousands of books and websites that provide a great depth of information about how to finance a business with loans. This document provides a quick

More information

8.1 Simple Interest and 8.2 Compound Interest

8.1 Simple Interest and 8.2 Compound Interest 8.1 Simple Interest and 8.2 Compound Interest When you open a bank account or invest money in a bank or financial institution the bank/financial institution pays you interest for the use of your money.

More information

HOW TO CALCULATE PRESENT VALUES

HOW TO CALCULATE PRESENT VALUES Chapter 2 HOW TO CALCULATE PRESENT VALUES Brealey, Myers, and Allen Principles of Corporate Finance 11th Edition McGraw-Hill/Irwin Copyright 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

More information

Credit cards UNCORRECTED PAGE PROOFS

Credit cards UNCORRECTED PAGE PROOFS Credit cards This chapter focuses on the use of credit cards as a method of payment for goods and services. The main mathematical ideas investigated are: interpreting credit card statements and performing

More information

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the Hewlett-Packard

More information

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM-09-05. April 28, 2014: Question and solutions 61 were added. January 14, 2014:

More information

A = P [ (1 + r/n) nt 1 ] (r/n)

A = P [ (1 + r/n) nt 1 ] (r/n) April 23 8.4 Annuities, Stocks and Bonds ---- Systematic Savings Annuity = sequence of equal payments made at equal time periods i.e. depositing $1000 at the end of every year into an IRA Value of an annuity

More information

LIABILITIES. Liabilities are claims against your Assets. They are something that you have to repay to someone else.

LIABILITIES. Liabilities are claims against your Assets. They are something that you have to repay to someone else. Accounting 101 ASSETS An Asset is something that you own, that has value, and will generate a future benefit. Assets are good. Eg.) Cash, accounts receivable, GST receivable, inventory, equipment, land,

More information

ACTIVITY 8.1 A MARGINAL PLAY

ACTIVITY 8.1 A MARGINAL PLAY LESSON 8 BUYING ON MARGIN AND SELLING SHORT ACTIVITY 8.1 A MARGINAL PLAY Stockbroker Luke, Katie, and Jeremy are sitting around a desk near a sign labeled Brokerage Office. The Moderator is standing in

More information

Percent, Sales Tax, & Discounts

Percent, Sales Tax, & Discounts Percent, Sales Tax, & Discounts Many applications involving percent are based on the following formula: Note that of implies multiplication. Suppose that the local sales tax rate is 7.5% and you purchase

More information

SECURITIES COMMISSION OF THE BAHAMAS PUBLIC NOTICE

SECURITIES COMMISSION OF THE BAHAMAS PUBLIC NOTICE SECURITIES COMMISSION OF THE BAHAMAS PUBLIC NOTICE No. 8 of 2010 December 1 st, 2010 FACTS RELATING TO THE CALCULATION OF THE RATE OF INTEREST TO BE CHARGED UNDER THE RATE OF INTEREST ACT, 1990 This NOTICE

More information

Chapter 2. CASH FLOW Objectives: To calculate the values of cash flows using the standard methods.. To evaluate alternatives and make reasonable

Chapter 2. CASH FLOW Objectives: To calculate the values of cash flows using the standard methods.. To evaluate alternatives and make reasonable Chapter 2 CASH FLOW Objectives: To calculate the values of cash flows using the standard methods To evaluate alternatives and make reasonable suggestions To simulate mathematical and real content situations

More information

Different Types of Loans

Different Types of Loans Different Types of Loans All loans, no matter what they are, are either secured or unsecured. Knowing the difference can better help you understand how they work and what to expect when applying for one.

More information

paid $71.50 for a 42-day $100 loan. That comes to roughly 621% APR if calculated as a closed-end payday loan would be.

paid $71.50 for a 42-day $100 loan. That comes to roughly 621% APR if calculated as a closed-end payday loan would be. Bank Payday Loan Products Jean Ann Fox, CFA August 7, 2009 Three major banks offer payday loan-type products to their checking account customers. U.S. Bank, Wells Fargo, and Fifth Third Bank offer open-end

More information

10.6 Functions - Compound Interest

10.6 Functions - Compound Interest 10.6 Functions - Compound Interest Objective: Calculate final account balances using the formulas for compound and continuous interest. An application of exponential functions is compound interest. When

More information

CONSUMER HANDBOOK ON ADJUSTABLE RATE MORTGAGES

CONSUMER HANDBOOK ON ADJUSTABLE RATE MORTGAGES CONSUMER HANDBOOK ON ADJUSTABLE RATE MORTGAGES This booklet was originally prepared by the Federal Reserve Board and the Office of Thrift Supervision in consultation with the following organizations: American

More information

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Interest Theory SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Interest Theory This page indicates changes made to Study Note FM-09-05. January 14, 2014: Questions and solutions 58 60 were

More information

Paying off a debt. Ethan D. Bolker Maura B. Mast. December 4, 2007

Paying off a debt. Ethan D. Bolker Maura B. Mast. December 4, 2007 Paying off a debt Ethan D. Bolker Maura B. Mast December 4, 2007 Plan Lecture notes Can you afford a mortgage? There s a $250,000 condominium you want to buy. You ve managed to scrape together $50,000

More information

Consumer Handbook on Adjustable Rate Mortgages

Consumer Handbook on Adjustable Rate Mortgages Consumer Handbook on Adjustable Rate Mortgages Federal Reserve Board Office of Thrift supervision EQUAL HOUSING OPPORTUNITY This booklet was prepared in consultation with the following organizations: American

More information

SAMPLE. MODULE 4 Principles of financial mathematics

SAMPLE. MODULE 4 Principles of financial mathematics C H A P T E R 20 MODULE 4 Principles of financial mathematics How do we determine the new price when discounts or increases are applied? How do we determine the percentage discount or increase applied

More information

Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices

Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices 196 Part Interest Rates and Valuing Cash Flows Chapter 6 APPENDIX B The Yield Curve and the Law of One Price Thus far, we have focused on the relationship between the price of an individual bond and its

More information

4 Annuities and Loans

4 Annuities and Loans 4 Annuities and Loans 4.1 Introduction In previous section, we discussed different methods for crediting interest, and we claimed that compound interest is the correct way to credit interest. This section

More information

UNIT 6 2 The Mortgage Amortization Schedule

UNIT 6 2 The Mortgage Amortization Schedule UNIT 6 2 The Mortgage Amortization Schedule A home mortgage is a contract that requires the homeowner to make a fixed number of monthly payments over the life of the mortgage. The duration, or length of

More information