1. Periodic Compound Interest

2. Annual Compound Interest

3. With interest for 1 year...

4. With interest for 2 years...

5. With interest for 3 years...

6. And so on...

7. Exponential Growth

8. Annual Interest

9. Example P = n = i = 24000 What values are given? 8 7/100 = 0.07

10. Calculate the new balance

11. Try Another

12. 12%, compounded quarterly Consider interest on our $10000 over a one- year period, but now compounded quarterly. Say the 12% is split into quarters so that 3% of interest is earned each quarter. Let i = interest per period = 0.12/4 = 0.03 n = number of times interest is computed = 4 Using the same compound interest formula, the new balance is computed to be

13. 12%, compounded monthly Consider interest on our $10000 over a one- year period, but now compounded monthly. Say the 12% is divided so that 1% of interest is earned each month. Let i = interest per period = 0.12/12 = 0.01 n = number of times interest is computed = 12 Using the same compound interest formula, the new balance is computed to be

14. Compound Interest Formula:

15. More frequent is better !

16. Keeps getting better !

17. Another Example

18. Avoid rounding errors !

19. Yet Another Example

20. A Different Question? The “Present Value”

21. Another Example

22. Comparing Interest Rates

23. Growth in 1 year?

24. Effectively, 9.6% Also, called the annual percentage yield (APY). The interest is equivalent to earning 9.6% annually.

25. Effectively, 9.74% This account has an effective rate, or APY, of 9.74%

26. Effective Rate Formula

27. Compare Accounts

28. Annual Yield Since the effective rate, r e, is the annual yield, use it like annual compounded interest ( m = 1). If a deposit of $8000 earns interest with an APY of 6.8%, what is the value of the account at the end of 5 years? Note an n th root is used to cancel an n th power.

29. Determining the Yield Suppose an investment of $9000 matures to a value of $12000 over 4 years. Determine the effective rate, r e, The APY is about 7.457%

30. Determining the Yield If a bond purchased for $700 matures to a value of $1200 over 8 years, what is the effective rate, r e. The APY is about 6.97%