1. Compound Interest

2. The interest is added to the principal and that amount becomes the principal for the next calculation of interest. OR

8. Interest Period (compounding Period): The amount of time which interest is calculated and added to the principal. It could be a year, a month, a week and so on.

11. Find the period interest rate for: A 12% annual interest rate with 4 interest periods per year. 3% An 18% annual rate with 12 interest periods per year. 1 ½ % An 8% annual rate with 4 interest periods per year. 2%

12. Find the Future Value Using the simple interest formula method: 1.Find the end of period principal: multiply the original principal by the sum of 1 and the period interest rate. 2.For each remaining period in turn, find the next end of period principal: multiply by the previous end of period principal by the sum of 1 and the period interest rate. 3.Identify the last end-of-period principal as the future value.

13. Look at this example Find the future value of a loan of $800 at 13% for three years. The period interest rate is 13% since it is calculated annually. First end-of-year = $800 x 1.13 = $904 Second end-of-year =$904 x 1.13 = $1021.52 Third end-of-year = $1021.52 x 1.13 = $1,154.32 The FV of this loan is $1,154.32

14. Find the compound interest Compound interest = future value – original principal. In the previous example, the compound interest is equal to the future value – original principal. CI = $1,154.32 - $800 = $354.32 The compound interest = $354.32

17. Derivation of the Formula = Amount at end of interest period + interest for period Amount at beginning of the interest period =P(1+i)+ iPPFirst year =P(1+i) 2 + iP(1+i)P(1+i)Second year =P(1+i) 3 + iP(1+i) 2 P(1+i) 2 Third year =P(1+i) n + iP(1+i) n-1 P(1+i) n-1 Nth year

26. Examples If 500$ were deposited in a bank savings account, how much would be in the account three years hence if the bank paid 6% interest compounded annually?

27. Examples If you wished to have 800$in a savings account at the end of four years, and 5% interest was paid annually, how much should you put into the savings account now?