1. Simple Interest 10 Mathematics 2015

2. Simple Interest You need to be able to use the simple interest formula to find INTEREST ($) PRINCIPAL ($) INTEREST RATE (% per annum) TIME (years) You also need to be able to convert time not given in years (ie. months, days, weeks) to a fraction of a year, and use this to find the 4 variables above

3. Simple Interest - What is it? If you borrow money, you must pay for the use of that money. If you lend money, you will be paid for doing so. The price of borrowing or lending money is called interest. The simplest type of interest is called simple interest. Suppose that we borrow $500 from a friend, and agree to pay him 10% interest for one year, after which time both the amount borrowed and the interest will be repaid. What does this mean? It means we will pay our friend $500, plus 10% of the amount borrowed, or at the end of the year a total of $550. If the money is borrowed or invested for several years, then interest may be paid or charged more than once. For example, if interest of 10% is charged per annum, then 10% of the amount borrowed is charged each year until the loan is repaid.

4. Simple Interest calculating interest (I) Simple Interest Formula To calculate simple interest (I), we need to know the amount invested or borrowed (P), the interest rate % (r) and the length of time (t) for which the money is invested or borrowed. Example: What is the simple interest paid on $2000 invested at 6% per annum for four years? P = $2000 r = 6 % per annum (this means 6% a year is paid in interest) t = 4 years (this needs to be in years or a fraction of a year) I = ?

5. What is the simple interest paid on $2000 invested at 6% per annum for four years? P = $2000 r = 6 % per annum t = 4 years I = ? Simple Interest Formula Simple Interest paid on the investment was $480

6. Simple Interest calculating the principal (P) Simple Interest Formula used to find principal (P) Sometimes you want to know the amount that has been borrowed or invested (P). This means we need to rearrange our formula to make P the subject. See the equation on the side. Example: Over a period of five years an investment earned $1070.25 at a simple interest rate of 5.45% per annum. What was the original amount deposited? P = ? r = 5.4% per annum t = 5 I = $1070.25

7. Example: Over a period of five years an investment earned $1070.25 at a simple interest rate of 5.45% per annum. What was the original amount deposited? P = ? r = 5.4% per annum t = 5 I = $1070.25 The original amount deposited was $3 963.89 Simple Interest Formula used to find principal (P)

8. Simple Interest calculating the interest rate (r) Simple Interest Formula used to find rate (r) Sometimes you want to know the amount that has been borrowed or invested (P). This means we need to rearrange our formula to make P the subject. See the equation on the side. Example: To buy his first car, Gary took out a personal loan for $3500. He paid it back over a period of two years and this cost him $1085 in interest. At what simple interest rate was he charged? P = $3500 r = ? t = 2 years I = $1085

9. Example: To buy his first car, Gary took out a personal loan for $3500. He paid it back over a period of two years and this cost him $1085 in interest. At what simple interest rate was he charged? P = $3500 r = ? t = 2 years I = $1085 The simple interest rate Gary borrowed at was 15.5% Simple Interest Formula used to find rate (r)

10. Simple Interest calculating the time invested (t) Simple Interest Formula used to find time (t) Sometimes you want to know the amount that has been borrowed or invested (P). This means we need to rearrange our formula to make P the subject. See the equation on the side. Example: If John invests $20 000 at 10% per annum until he has $32 000, for how many years will he have to invest the money? P = $20 000 r = 10% per annum t = ? I = ($32 000 - $20 000) = $12 000

11. Example: If John invests $20 000 at 10% per annum until he has $32 000, for how many years will he have to invest the money? P = $20 000 r = 10% per annum t = ? I = ($32 000 - $20 000) = $12 000 John would have to invest for 6 years Simple Interest Formula used to find time (t)

12. Simple Interest – more complicated Sometimes within simple interest questions you might be given a time period that is not a year, before finding simple interest you need to convert this time into a fraction of a year. Example: What is the simple interest on $10 000 invested at 6% per annum for eight months P = $10 000 r = 6 % per annum t = of a year I = ?