1. Exercise Write 5% as a decimal. 0.05

2. Write 6.5% as a decimal. 0.065 Exercise

3. What fraction of a year is 9 months? 3434 3434 Exercise

4. What fraction of a year is 8 months? 2323 2323 Exercise

5. 3,000(0.045)( ) 90 2323 2323 Exercise

6. 4(1 + 0.1) 2 4.84 Exercise

7. Simple Interest Formula I = P r t, where I = interest, P = principal, r = annual rate of interest, and t = time in years.

8. Find the simple interest earned from a one-time investment of $3,000 at 8% interest if the account is closed at the end of 2 years. I = Prt = $480 Example 1 = 3,000(0.08)(2)

9. Aaron borrowed $465 for 1 year. His bank gave him a simple interest loan at 12% annual interest for 1 year. How much interest will he pay? I = Prt Aaron owes $55.80 simple interest on this loan. Example 2 = 465(0.12)(1) = 55.80

10. How much interest is owed at the end of two years on a loan of $500 at 9% simple interest? $90 Example

11. Amount Formula A = P + I, where A = amount due, P = principal, and I = interest.

12. Find the interest and the total value of an investment of $1,500 at 5% simple interest for 9 months. t = 9 12 == 3434 3434 = 0.75 I = Prt A = P + I = $1,556.25 Example 3 = 1,500(.05)(.75) = 56.25 = 1,500 + 56.25

13. What is the total amount owed at the end of two years on a loan of $500 at 9% simple interest? $590 Example

14. Compound interest – money paid on both the principal and previous interest earned

15. Interval annually Meaning # # semiannually quarterly monthly every year every six months 12 44 22 11 every three months every month

16. 4,000(0.03)(1) = $120 4,000(0.03)(0.25) = $30 4,000 + 30 = $4,030 4,030(0.30)(0.25) = $30.23 4,030 + 30.23 = $4,060.23

17. 4,060.23(0.03)(0.25) = $30.45 4,060.23 + 30.45 = $4,090.68 4,090.68(0.30)(0.25) = $30.68 4,090.68 + 30.68 = $4,121.36 4,121.36 – 4,000 = $121.36

18. A savings account offers 4% interest compounded monthly. Find the amount in the account at the end of 3 mo. if the initial deposit is $10,000. How much interest was earned during the first 3 mo.? Example 4

19. Since the interest is computed monthly, let t =. 1 12 Use a calculator to multiply the principal times 0.04; then divide the product by 12. Remember to round to the nearest cent.

20. Period Principal Interest New Principal $10,000 = $10,033.33 11 ≈ $33.33 10,000 + 33.33 10,000(.04)( ) 1 12

21. Period Principal Interest New Principal $10,033.33 = $10,066.77 22 ≈ $33.44 10,033.33 + 33.44 10,033.33(.04)( ) 1 12

22. Period Principal Interest New Principal $10,066.77 = $10,100.33 33 ≈ $33.56 10,066.77 + 33.56 10,066.77(.04)( ) 1 12

23. The amount of interest earned was 10,100.33 – 10,000 = $100.33.

24. An investment pays 8% interest compounded annually. How much interest is paid on a deposit of $1,000 left in for two years? $166.40 Example

25. How much interest would that same $1,000 earn in two years at 8% if simple interest was used? $160 Example

26. Annual Compound Interest Formula S = P(1 + i) n, where S = amount in the savings account, P = principal, i = annual interest rate, and n = number of annual interest payments.

27. Use a calculator to find the amount in a savings account at the end of 5 yr. if $5,200 is invested at 3.5% interest compounded annually. Also, find the amount of interest earned. Example 5

28. P = $5,200i = 3.5% = 0.035n = 5 S = P(1 + i) n S = 5,200(1 + 0.035) 5 S = 5,200(1.035) 5 S = 5,200(1.87686306) S = $6,175.97 6,175.97 – 5,200= $975.97

29. What is the interest earned on $1,000 at 8% over a time period of twenty years compounded annually? What is the simple interest earned over twenty years? $3,660.96; $1,600 Example

30. What would the interest be on $1,000 over a twenty-year period at 8% compounded quarterly? $3,875.44 Example