Section10.1.notebook May 24, 2014

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1 Unit 9 Borrowing Money 1

2 Most people will need to take out a loan sometime in their lives. Few people can afford expensive purchases such as a car or a house without borrowing money from a financial institution. Sometimes, these loans are paid back in one lump sum after a period of time. However, most of the time, loans are paid back on a schedule, with payments being made weekly, bi weekly, monthly, etc. In this lesson, we will look at loan payments in both situations. Simple vs. Compound Interest Simple Interest: the amount of interest that you receive (if investing) or pay on a loan is calculated ONLY on the amount of money that you borrow. Usually loans from personal friends, family (NEVER BANKS!) An investment of $1000 at 5% simple interest per annum may look like 2

3 Compound Interest: interest is paid on two different things: (i) the amount of money that you borrow and (ii) the interest that you pay on the money that you borrowed. Usually Banks An Investment: $1000 at 5% per annum for 4 years looks like 3

4 When we talk about borrowing money, there are two groups of people involved: 1. The customer (person/group who borrows the money). 2. The lender (the person/institution who loans out the money. It may be a friend, a family member, bank, etc.). There are two main factors that affect the advantages and disadvantages of different types of interest: 1. Whether you are a customer or lender: ie. compound interest is an advantage for a lender since they will earn more money in interest, but a disadvantage for a customer however because it means they will pay out more in interest. 2. Whether you are borrowing or investing money: simple interest would be better for a customer who is borrowing money since it results in the customer having to pay out less money in interest. However, compound interest is better for a customer who is investing money since it means they will gain more money on their investment through interest. Loans are often offered at an interest rate that is compounded. Therefore, before we begin looking at loans, we need to review some of the financial concepts learned in Unit 6. 4

5 There are two types of interest: simple and compound. For simple interest, only the initial principal earns interest. The formula for simple interest is where A represents the amount present P represents the principal amount r = interest rate divided by 100 t represents the number of years Simple interest increases linearly (at a constant rate) over time For compound interest, the initial principal and accumulated interest also gain interest. The formula is where P is the principal amount i is the interest rate per compounding period n is the number of compounding periods Notice that i is the interest rate per compounding period. If interest is compounded x times each year, then the given percentage must be divided by x to come up with i. 5

6 Recall that compound interest may be compounded: daily (every day or 365periods a year) weekly (every week or 52 periods a year) semi monthly (twice a month or 24 periods a year) bi weekly (every two weeks or 26 periods a year) monthly (every month or 12 periods a year) quarterly (every 3 months or 4 periods a year) semi annually (every 6 months or 2 periods a year) annually (once every year) 6

7 Ralph invested his summer earnings of $6000 at 4% simple interest, paid annually. Determine the relation that models this situation and use it to determine: (a) the value of the investment after 20 years. (b) when the investment will be worth $

8 Which investment would yield a greater return for 10 years Option 1: $1000 at 3.5% annual simple interest Option 2: $1000 at 3% annual compound interest Conclusion: 8

9 James intends to go to university. His Grandmother would like to invest $2000 in a GIC [Guaranteed Investment Certificate] A) How much will the GIC be worth if it is invested at 3% simple interest for 5 years? B) How much would it be worth if the interest was compounded? C) Which option is better for the bank? For James? 9

10 A person takes out a $2000 loan, compounded at 10% semi annually. When the person pays back the loan in one lump sum, he owes $ Determine how much time the person had the loan for. 10

11 Shianne put money in the bank which gained interest at a rate of 5% compounded annually. After 7 years, she had $ in the bank. Determine the initial amount of money she put in the bank. 11

12 Annette wants to borrow money to renovate her kitchen. Her bank will charge her 3.6% compounded quarterly. Annette wants to pay back the money with one lump payment after 3 years, and wants this payment to be at most $ Determine the maximum amount of money she can borrow. 12

13 When a financial institution lends money, it will always negotiate the terms of the loan, including the interest rate and how it wants the money paid back. We will consider two cases: Paying Back Loans (Part 1) 1. A loan is paid off using a single payment at the end of the term. 2. A loan is paid off by making regular loan payments (only cases in which payment frequency matches the compounding period). We will start off by looking at loans that are paid off using a single payment at the end of the term. Examples: a farmer making a single lump sum payment on his loan after his crop has been harvested a payday loan offered by certain financial service providers. We have already dealt with these types of problems. Note: Interest Paid = A - P OR I = A - P 13

14 Trina s employer loaned her $10000 at a fixed interest rate of 6%, compounded annually, to pay for college tuition and textbooks. The loan is to be repaid in a single payment on the maturity date, which is at the end of 5 years. Determine how much interest Trina will pay on the loan. 14

15 A credit card company charges an interest rate of 14%, compounded monthly. If a person charges $300 to the card and does not pay it off, how much interest is the person charged after one year? 15

16 Mary borrows $1000 at 10% interest, compounded semi annually. Sean borrows $1000 at 10% interest compounded annually. How much interest will each pay at the end of two years? 16

17 The more frequent the compounding, the more interest will be charged. When making financial decisions, it is important to understand the rate of interest charged, as well as the compounding, as these can create large differences over long periods of time. Which represents the lowest interest that would be paid? (A) 10% compounded daily (B) 10% compounded monthly (C) 10% compounded annually 17

18 Which represents the lowest interest that would be paid? (A) 8% compounded daily (B) 12% compounded monthly 18