1. Personal Finance How to avoid a bad bargain!

2. Comparing interest rates Alexandra has £1000 to invest. Which scheme should she choose? 6% per annum 3% over 6 months

3. Long term saving Every January for 5 years, Alexandra invests her annual savings of £1000 and is paid at an annual rate of interest of 6 percent. If she has £S k at the start of year k, how much will she have a year later? 6% per annum

4. Borrowing money ONLY 1.26% per month ONLY 8.4% per annum EASY FINANCE Borrow £5000 under our PRIVILEGED CUSTOMER SCHEME and pay just £451.55 per month for one year 16.2% APR

5. APR The Annual Percentage Rate (APR) is the rate you would pay if you paid the whole lot back at the end of the year. Regulations require this rate to be quoted on all deals so that you can compare them. To calculate it, consider the total interest over the year if it is added to the loan each month.

6. To investigate… 1.Find the APR that corresponds to a monthly interest rate of (a) 1%(b) 2%(c) 5% 2.Write down a rule for converting monthly interest rates to APR 3.Use this method, and trial and improvement, to work out the monthly interest rate that corresponds to an APR of 100% 4.A loan of £1200 is repaid by 6 monthly installments of £212. What is the APR? (Use a spreadsheet!) 5.For an APR of 15%, design a hire purchase agreement for a car costing £9 987.37 ‘on the road’, requiring a 30% deposit and payment over 3 years. You should make all the payments clear, including any final payment necessary (usually called a ‘terminal rental’).

7. mortgages A mortgage is a cheaper way of borrowing money. Something solid and valuable, usually a house, is used as security on the loan, so that if you default on the payments, the bank can take the house. This means less risk for the bank, so they can offer lower rates. Usually a mortgage is taken out to purchase the house used as security, but if you already own a house and don’t owe any money on it, you can take out a mortgage for some other purpose, perhaps to fund a business initiative.

8. Mortgage types There are 2 types of mortgage: ‘repayment’ and ‘interest only’ Repayment mortgages You pay enough each month that at the end of the period (often 25 years), you owe nothing Interest only mortgages You just pay the interest, and need to find a way to pay off the capital at the end of the period

9. Repayment mortgages To work out how a repayment mortgage works, take a simple example: Borrow £90 000 at 10% per annum How long will it take to repay the loan?

10. Repayment mortgages YEAR ONE:Initial loan90 000 Interest 9 000 Total debt99 000 Repayments 12 @ 90010 800 Outstanding balance88 200

11. Repayment mortgages 1.Set out the working you do for the amount owing at the end of year 1 as a single calculation. 2.Do the same for year 2, but substitute in the calculation for year 1 in rather than the value. 3.Repeat for years 3, 4 etc until you can see a pattern. 4.Write down an expression for the amount owed after n years, using sigma notation. 5.Simplify this expression using your knowledge of summing series. 6.Hence find the monthly payment required to clear the debt after 25 years.

12. Repayment mortgages Repeat the previous exercise for the loan you need to buy the house of your choice at current prices and interest rates!! Note that you are generally required to pay a deposit of around 5% of the value of the house.