Lesson 24 Annuities. Minds On

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1 Lesson 24 Annuities Goals To define define and understand how annuities work. To understand how investments, loans and mortgages work. To analyze and solve annuities in real world situations (loans, investments). Minds On How is this question different from the ones we have solved so far?

2 Where does this type of application connect in our daily lives? What is "credit"? The ability of a customer to obtain goods or services before payment, based on the trust that payment will be made in the future. Credit comes in many forms: credit cards loans (line of credit, car loan, OSAP) mortgages

3 What is a "credit score"? A credit score is a three digit number calculated from your credit report and is one factor used by lenders to determine your credit worthiness for a mortgage, loan or credit card. Your score can affect whether or not you are approved as well as what interest rate you are charged. Your credit score is a number between 300 and 850. It is based upon: 1) Payment history late payments, debts in collection 2) Use of available credit the percentage of credit available to you that you USE (lower is better!) 3) Length of Credit History how long you have had a given account or credit card (older is better!) 4) Number of Inquiries how many times you apply for credit within a given time frame 5) Types of Credit the number of different accounts you have (ie. VISA and Mastercard, car loan, mortgage, etc.) Your debt to income ratio is also a part of your credit score. This is an important consideration when you graduate from post secondary with debt and no job! Credit Cards How they work: You must be 18 years or older to apply for a credit card. A credit limit is given to the cardholder based on their credit score and yearly income. Interest is charged yearly. It is referred to as the APR (Annual Percentage Rate). It is usually between %. Interest is compounded DAILY. You usually have a grace period of 21 to 30 days before interest charges are applied. You may carry a balance owing on your credit card. You must pay a minimum payment each month that will be equal to the interest charges plus a small payment on the principal debt. Big box store "Pay Later" programs work the same way.

4 Loans How they work: You apply to borrow a specific amount of money for a purpose that is approved by the bank. (Purchase of a car, home renovation, education). You will be offered an interest rate based on your credit score and the posted rate. You will also be required to determine the repayment terms (number of payments and amount of the regular payment). The posted rate depends on the interest rate, set by The Bank of Canada. Today the lending rate is 0.5%. The rate set by a given lender (ie. TD bank) is called "prime". It fluctuates from day to day and is easy to obtain online. service/todays rates/rates.jsp Mortgages How they work: A mortgage is a special type of loan used for the purchase of homes and buildings (major assets). They are special because the repayment period is long (5 25 years). The length of the repayment period is called the amortization. The interest rate depends on prime, and your credit score. Some people hire a mortgage broker to find them the best rate. The frequency of regular payments is typically monthly, bimonthly, or weekly. A minimum down payment of 5% of the house price is required. All down payments less than 20% require the homeowner to purchase mortgage default insurance (CHMC insurance).

5 Student Loans There are two ways to borrow money for educational purposes in Canada. The government provides loans that are interestfree until graduation, through the OSAP program. Private banks also offer student loans, however these loans are not interest free and have rates similar to personal lines of credit. The formulas we use to solve annuities are complex and require multiple algebraic steps to solve for one of the given variables. When we are using annuities we usually want to solve for things like: What is the monthly payment if I borrow a given amount? What is the monthly payment if I want to save a given amount? What is the interest rate I need? How many payments will be required? How much interest will I be paying?

6 To rearrange the formulas each time is a lot of work! So most people working in finances (banks, accounting, etc) rely on TECHNOLOGY to solve these types of problems. They use Time Value of Money (TVM) Solvers. We will use the Graphing Calculator TVM Solver to do this.

7 Follow the instructions to start your TVM Solver. Once you have the TVM Solver open you should see the screen shown below. interest rate per year (%) future value number of payments present value regular payment payment per year and compounding periods per year Example 1 Max loves money and decides that he is going to save $50 per month in a mutual fund that guarantees 2.1% interest per year, compounded monthly, starting on his 12th birthday. a. How much money will Max have when he is 65 if he never misses a payment? b. How much interest did Max earn?

8 Example 2 Jen is buying her first home and has negotiated a purchase price of $ She has a $ down payment. She has negotiated an interest rate of 3.8% per year, compounded monthly, and has amortized the mortgage for 25 years. a. What is her monthly payment? b. What will she end up paying the bank for her home with this rate and payment? Example 3 Adam has just graduated from university and has accumulated a student loan debt of $ His loan documents indicate that he will pay a monthly repayment at a rate of 4.5% /a, compounded monthly. a. What is the monthly payment if he pays student loan off in: i) 5 years ii) 10 years iii) 15 years b. What is the difference in the amount of interest he will pay in each case?

9 Practice Section 8.6, pages , #1 3, 5