1. 1 Learning Objectives for Section 3.1 Simple Interest After this lecture, you should be able to Compute simple interest using the simple interest formula. Solve problems involving investments and the simple interest formula.

2. 2 Some Preliminary Notes Financial institutions often use 360 days for one year when computing time. Time must be in terms of years to use in the formulas. All rates (%) must be converted to decimals to use in formulas. When an answer is rounded, use the symbol  instead of =. We will round to the nearest cent for dollar amounts, unless otherwise stated. Try to avoid rounding until the final answer.

3. 3 Conversions: Time Periods Example 1: Convert the given time periods into years: a)180 daysb) 120 daysc) 3 quarters d) 7 monthse) 60 daysf) 26 weeks

4. 4 Conversions: Percents to Decimals Example 2: Convert the given percents to decimals: a)4.5%b).32%c) 112%

5. 5 Conversions: Decimals to Percents Example 3: Convert the given decimals to percents: a) 0.06b) 5c) 0.11

6. 6 Simple Interest Formula where I = interest P = principal (amount invested or amount of loan) r = annual simple interest rate (as a decimal) t = time in years

7. 7 An Example Example 4: Find the interest on a boat loan of $5,000 at 16% for 8 months. Example 5: What is the total amount to be paid back on the boat loan in Example 4?

8. 8 Total Amount to Be Paid Back In general, the future value (amount) is given by the following equation: A = Principal + Interest A = P + I A = P + Prt A = P (1 + rt)

9. 9 Another Example Example 6: Find the total amount due on a loan of $600 at 16% interest at the end of 15 months.

10. 10 Another Example Example 7: A loan of $10,000 was repaid at the end of 6 months. What amount (principal and interest) was repaid, if a 6.5% annual rate of interest was charged?

11. 11 Application Example 8: A department store charges 18.6% interest (annual) for overdue accounts. How much interest will be owed on a $1,080 account that is 3 months overdue?

12. 12 Interest Rate Earned on a Note Example 9: What is the annual interest rate earned by a 33-day T-bill with a maturity value of $1,000 that sells for $996.16?

13. 13 Purchase Price of a Note Example 10: What is the purchase price of a 26-week T-bill with a maturity value of $1,000 that earns an annual interest rate of 4.903%?